Question 1

Solve the equation. $$5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }$$

Accepted Answer

A) {1} 
B) {0, 9} 
C) {3} 
D) {0, 3} 
E) {-3} 
A) {1} 
B) {0, 9} 
C) {3} 
D) {0, 3} 
E) {-3} E

Question 2

Solve the equation. $$\frac { 2 y - 10 } { 8 y ^ { 2 } + 18 y - 18 } - \frac { 4 } { 2 y + 6 } = \frac { 4 } { 4 y - 3 }$$

Accepted Answer

A) { 0, 1 } 
B) { 0, -1 } 
C) { 0 } 
D) { -1 } 
E) { 1 } 
A) { 0, 1 } 
B) { 0, -1 } 
C) { 0 } 
D) { -1 } 
E) { 1 } D

Question 3

Perform the indicated division and express your answer in simplest form. $\frac { 2 y ^ { 2 } - 3 y - 20 } { ( y - 4 ) ^ { 2 } } \div \frac { 2 y ^ { 2 } + 13 y + 20 } { 2 y ^ { 2 } - 7 y - 4 }$

Accepted Answer

A)  $\frac { y - 4 } { 2 y + 1 }$ 
B)  $\frac { y + 4 } { 2 y + 1 }$ 
C)  $\frac { 2 y + 1 } { y - 4 }$ 
D)  $\frac { 2 y - 1 } { y + 4 }$ 
E)  $\frac { 2 y + 1 } { y + 4 }$ 
A)  $\frac { y - 4 } { 2 y + 1 }$ 
B)  $\frac { y + 4 } { 2 y + 1 }$ 
C)  $\frac { 2 y + 1 } { y - 4 }$ 
D)  $\frac { 2 y - 1 } { y + 4 }$ 
E)  $\frac { 2 y + 1 } { y + 4 }$ E

Question 4

Simplify the fraction to lowest terms. $\frac { 3,500 } { 1,500 }$

Accepted Answer

A)  $\frac { 7 } { 3 }$ 
B)  $\frac { 70 } { 30 }$ 
C)  $\frac { 3,500 } { 1,500 }$ 
D)  $\frac { 35 } { 15 }$ 
E)  $\frac { 3 } { 7 }$ 
A)  $\frac { 7 } { 3 }$ 
B)  $\frac { 70 } { 30 }$ 
C)  $\frac { 3,500 } { 1,500 }$ 
D)  $\frac { 35 } { 15 }$ 
E)  $\frac { 3 } { 7 }$

Question 5

Solve the following equation for the variable x . $$y = \frac { 4 } { 5 } x + \frac { 5 } { 20 }$$

Accepted Answer

A)  $$x = - \frac { 5 } { 4 } y + \frac { 5 } { 16 }$$ 
B)  $x = \frac { 5 } { 4 } y + \frac { 5 } { 4 }$ 
C)  $x = \frac { 5 } { 4 } y - \frac { 5 } { 16 }$ 
D)  $x = \frac { 5 } { 4 } y - \frac { 5 } { 20 }$ 
E)  $x = \frac { 5 } { 4 } y + \frac { 5 } { 20 }$ 
A)  $$x = - \frac { 5 } { 4 } y + \frac { 5 } { 16 }$$ 
B)  $x = \frac { 5 } { 4 } y + \frac { 5 } { 4 }$ 
C)  $x = \frac { 5 } { 4 } y - \frac { 5 } { 16 }$ 
D)  $x = \frac { 5 } { 4 } y - \frac { 5 } { 20 }$ 
E)  $x = \frac { 5 } { 4 } y + \frac { 5 } { 20 }$

Question 6

Solve the following equation for the variable x . $y = - \frac { l } { g } x + \frac { e } { n }$

Accepted Answer

A)  $x = \frac { g e - g n y } { \lg }$ 
B)  $x = \frac { l n + g n y } { e n }$ 
C)  $x = \frac { g e - g n y } { \ln }$ 
D)  $x = y \left( \frac { g } { l } - \frac { n } { e } \right)$ 
E)  $x = y \left( \frac { g e - g n } { \ln } \right)$ 
A)  $x = \frac { g e - g n y } { \lg }$ 
B)  $x = \frac { l n + g n y } { e n }$ 
C)  $x = \frac { g e - g n y } { \ln }$ 
D)  $x = y \left( \frac { g } { l } - \frac { n } { e } \right)$ 
E)  $x = y \left( \frac { g e - g n } { \ln } \right)$

Question 7

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.)Round your answer to the nearest integer.

Accepted Answer

A) x = 870 ft 
B) x = 813 ft 
C) x = 845 ft 
D) x = 885 ft 
E) x = 833 ft 
A) x = 870 ft 
B) x = 813 ft 
C) x = 845 ft 
D) x = 885 ft 
E) x = 833 ft

Question 8

Perform the division. $\frac { - 10 a ^ { 2 } b ^ { 2 } - 20 a ^ { 2 } b - 15 a b ^ { 2 } } { - 5 a b }$

Accepted Answer

A)  $3 a b + 5 a + 3 b$ 
B)  $3 a b + 4 a + 3 b$ 
C)  $2 a b + 5 a + 3 b$ 
D)  $2 a b + 4 a + 4 b$ 
E)  $2 a b + 4 a + 3 b$ 
A)  $3 a b + 5 a + 3 b$ 
B)  $3 a b + 4 a + 3 b$ 
C)  $2 a b + 5 a + 3 b$ 
D)  $2 a b + 4 a + 4 b$ 
E)  $2 a b + 4 a + 3 b$

Question 9

Solve for the variable in the proportion. $\frac { x + 2 } { 4 } = \frac { 6 } { 12 }$

Accepted Answer

A)  $x = 1$ 
B)  $x = - 2$ 
C)  $x = 3$ 
D)  $x = - 1$ 
E)  $x = 0$ 
A)  $x = 1$ 
B)  $x = - 2$ 
C)  $x = 3$ 
D)  $x = - 1$ 
E)  $x = 0$

Question 10

Find the quotient. $\frac { 5 } { 2 } \div \left( - \frac { 3 } { 7 } \right)$

Accepted Answer

A)  $\frac { 40 } { 5 }$ 
B)  $- \frac { 36 } { 11 }$ 
C)  $- \frac { 39 } { 3 }$ 
D)  $- \frac { 34 } { 10 }$ 
E)  $- \frac { 35 } { 6 }$ 
A)  $\frac { 40 } { 5 }$ 
B)  $- \frac { 36 } { 11 }$ 
C)  $- \frac { 39 } { 3 }$ 
D)  $- \frac { 34 } { 10 }$ 
E)  $- \frac { 35 } { 6 }$

Question 11

Multiply and reduce your answer to lowest terms. $- \frac { 42 } { 5 } \cdot \frac { 7 } { 21 } \cdot \frac { 1 } { 14 }$

Accepted Answer

A)  $- \frac { 1 } { 5 }$ 
B)  $\frac { 1 } { 5 }$ 
C) -1 
D) 1 
E)  $- \frac { 5 } { 5 }$ 
A)  $- \frac { 1 } { 5 }$ 
B)  $\frac { 1 } { 5 }$ 
C) -1 
D) 1 
E)  $- \frac { 5 } { 5 }$

Question 12

Solve the equation. $\frac { 3 a - 9 } { 6 } + \frac { 4 a - 4 } { 4 } + \frac { 3 a + 9 } { 4 } = 11$

Accepted Answer

A) a = 10 
B) a = -5 
C) a = 2 
D) a = 5 
E) a = 8 
A) a = 10 
B) a = -5 
C) a = 2 
D) a = 5 
E) a = 8

Question 13

Perform the indicated operation and express your answer in simplest form. $\frac { 6 } { x ^ { 2 } - 5 x - 24 } - \frac { 1 } { x ^ { 2 } - 3 x - 40 }$

Accepted Answer

A)  $\frac { x + 27 } { ( x - 8 ) ( x - 3 ) ( x - 5 ) }$ 
B)  $\frac { 5 x + 27 } { ( x - 8 ) ( x + 3 ) ( x - 5 ) }$ 
C)  $\frac { 5 x + 27 } { ( x - 8 ) ( x + 3 ) ( x + 5 ) }$ 
D)  $\frac { 5 x + 27 } { ( x - 8 ) ( x - 3 ) ( x + 5 ) }$ 
E)  $\frac { x + 5 } { ( x - 8 ) ( x - 3 ) ( x - 5 ) }$ 
A)  $\frac { x + 27 } { ( x - 8 ) ( x - 3 ) ( x - 5 ) }$ 
B)  $\frac { 5 x + 27 } { ( x - 8 ) ( x + 3 ) ( x - 5 ) }$ 
C)  $\frac { 5 x + 27 } { ( x - 8 ) ( x + 3 ) ( x + 5 ) }$ 
D)  $\frac { 5 x + 27 } { ( x - 8 ) ( x - 3 ) ( x + 5 ) }$ 
E)  $\frac { x + 5 } { ( x - 8 ) ( x - 3 ) ( x - 5 ) }$

Question 14

Solve the following equation for the variable y . $- \frac { 2 } { x - 4 } = \frac { 3 } { y - 1 }$

Accepted Answer

A)  $y = - \frac { 2 } { 3 } x + 7$ 
B)  $y = \frac { 3 } { 2 } x + 7$ 
C)  $y = \frac { 2 } { 3 } x - 7$ 
D)  $y = - \frac { 2 } { 3 } x - 7$ 
E)  $y = - \frac { 3 } { 2 } x + 7$ 
A)  $y = - \frac { 2 } { 3 } x + 7$ 
B)  $y = \frac { 3 } { 2 } x + 7$ 
C)  $y = \frac { 2 } { 3 } x - 7$ 
D)  $y = - \frac { 2 } { 3 } x - 7$ 
E)  $y = - \frac { 3 } { 2 } x + 7$

Question 15

Solve the equation. $$3 + \frac { 12 } { t - 7 } = \frac { 12 } { t ( t - 7 ) }$$

Accepted Answer

A) {3, -1 } 
B) { -1} 
C) {3} 
D) {4, -1} 
E) {-3, 1} 
A) {3, -1 } 
B) { -1} 
C) {3} 
D) {4, -1} 
E) {-3, 1}

Question 16

Perform the multiplication. Simplify the answer, if possible. $\frac { 2 z - 4 } { z + 2 } \cdot \frac { 5 } { 5 z - 10 }$

Accepted Answer

A)  $\frac { 2 } { z - 2 }$ 
B)  $\frac { 5 } { z - 2 }$ 
C)  $\frac { z - 2 } { 5 }$ 
D)  $\frac { 5 } { z + 2 }$ 
E)  $\frac { 2 } { z + 2 }$ 
A)  $\frac { 2 } { z - 2 }$ 
B)  $\frac { 5 } { z - 2 }$ 
C)  $\frac { z - 2 } { 5 }$ 
D)  $\frac { 5 } { z + 2 }$ 
E)  $\frac { 2 } { z + 2 }$

Question 17

Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole.   a = 11, b = 7, c = 31

Accepted Answer

A)  $14$ ft 
B)  $21$ ft 
C)  $19 \frac { 8 } { 11 } \mathrm { ft }$ 
D)  $22 \frac { 8 } { 11 } \mathrm { ft }$ 
A)  $14$ ft 
B)  $21$ ft 
C)  $19 \frac { 8 } { 11 } \mathrm { ft }$ 
D)  $22 \frac { 8 } { 11 } \mathrm { ft }$

Question 18

Perform the operations. $\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }$

Accepted Answer

A)  $\frac { 2 } { s - 10 }$ 
B)  $\frac { 2 } { s + 4 }$ 
C)  $\frac { 2 } { s + 10 }$ 
D)  $\frac { 2 } { s - 20 }$ 
E)  $\frac { 1 } { s - 10 }$ 
A)  $\frac { 2 } { s - 10 }$ 
B)  $\frac { 2 } { s + 4 }$ 
C)  $\frac { 2 } { s + 10 }$ 
D)  $\frac { 2 } { s - 20 }$ 
E)  $\frac { 1 } { s - 10 }$

Question 19

Simplify the complex fraction. $\frac { - \frac { 7 } { x } - \frac { 14 } { x + 7 } } { \frac { 2 } { x ^ { 2 } + 7 x } + \frac { 2 } { x } }$

Accepted Answer

A)  $- \frac { x + 7 } { 2 ( x + 8 ) }$ 
B)  $- \frac { 3 x - 7 } { 7 ( x + 8 ) }$ 
C)  $- \frac { 7 ( 3 x - 7 ) } { 2 ( x + 8 ) }$ 
D)  $- \frac { 2 ( 3 x - 7 ) } { 7 ( x + 8 ) }$ 
E)  $- \frac { 7 ( 3 x - 7 ) } { 2 ( x + 8 ) }$ 
A)  $- \frac { x + 7 } { 2 ( x + 8 ) }$ 
B)  $- \frac { 3 x - 7 } { 7 ( x + 8 ) }$ 
C)  $- \frac { 7 ( 3 x - 7 ) } { 2 ( x + 8 ) }$ 
D)  $- \frac { 2 ( 3 x - 7 ) } { 7 ( x + 8 ) }$ 
E)  $- \frac { 7 ( 3 x - 7 ) } { 2 ( x + 8 ) }$

Question 20

Perform the indicated operation and express your answer in simplest form. $\frac { 11 x + 41 } { x ^ { 2 } - 9 } - \frac { 6 } { x - 3 }$

Accepted Answer

A)  $\frac { 11 x + 23 } { ( x + 3 ) ( x - 3 ) }$ 
B)  $\frac { 5 x - 23 } { ( x + 3 ) ( x - 3 ) }$ 
C)  $\frac { 5 x - 23 } { x + 3 }$ 
D)  $\frac { 5 x + 23 } { ( x + 3 ) ( x - 3 ) }$ 
E)  $\frac { 5 x - 23 } { x - 3 }$ 
A)  $\frac { 11 x + 23 } { ( x + 3 ) ( x - 3 ) }$ 
B)  $\frac { 5 x - 23 } { ( x + 3 ) ( x - 3 ) }$ 
C)  $\frac { 5 x - 23 } { x + 3 }$ 
D)  $\frac { 5 x + 23 } { ( x + 3 ) ( x - 3 ) }$ 
E)  $\frac { 5 x - 23 } { x - 3 }$

Solve the equation. $5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }$

Solve the equation. $\frac { 2 y - 10 } { 8 y ^ { 2 } + 18 y - 18 } - \frac { 4 } { 2 y + 6 } = \frac { 4 } { 4 y - 3 }$

Perform the indicated division and express your answer in simplest form. $\frac { 2 y ^ { 2 } - 3 y - 20 } { ( y - 4 ) ^ { 2 } } \div \frac { 2 y ^ { 2 } + 13 y + 20 } { 2 y ^ { 2 } - 7 y - 4 }$

Simplify the fraction to lowest terms. $\frac { 3,500 } { 1,500 }$

Solve the following equation for the variable x . $y = \frac { 4 } { 5 } x + \frac { 5 } { 20 }$

Solve the following equation for the variable x . $y = - \frac { l } { g } x + \frac { e } { n }$

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.)Round your answer to the nearest integer.

Perform the division. $\frac { - 10 a ^ { 2 } b ^ { 2 } - 20 a ^ { 2 } b - 15 a b ^ { 2 } } { - 5 a b }$

Solve for the variable in the proportion. $\frac { x + 2 } { 4 } = \frac { 6 } { 12 }$

Find the quotient. $\frac { 5 } { 2 } \div \left( - \frac { 3 } { 7 } \right)$

Multiply and reduce your answer to lowest terms. $- \frac { 42 } { 5 } \cdot \frac { 7 } { 21 } \cdot \frac { 1 } { 14 }$

Solve the equation. $\frac { 3 a - 9 } { 6 } + \frac { 4 a - 4 } { 4 } + \frac { 3 a + 9 } { 4 } = 11$

Perform the indicated operation and express your answer in simplest form. $\frac { 6 } { x ^ { 2 } - 5 x - 24 } - \frac { 1 } { x ^ { 2 } - 3 x - 40 }$

Solve the following equation for the variable y . $- \frac { 2 } { x - 4 } = \frac { 3 } { y - 1 }$

Solve the equation. $3 + \frac { 12 } { t - 7 } = \frac { 12 } { t ( t - 7 ) }$

Perform the multiplication. Simplify the answer, if possible. $\frac { 2 z - 4 } { z + 2 } \cdot \frac { 5 } { 5 z - 10 }$

Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. a = 11, b = 7, c = 31

Perform the operations. $\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }$

Simplify the complex fraction. $\frac { - \frac { 7 } { x } - \frac { 14 } { x + 7 } } { \frac { 2 } { x ^ { 2 } + 7 x } + \frac { 2 } { x } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 11 x + 41 } { x ^ { 2 } - 9 } - \frac { 6 } { x - 3 }$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 4: Rational Expressions

Solve the equation. 5+25n−5=125n2−5n5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }5+n−525​=n2−5n125​

Solve the equation. 2y−108y2+18y−18−42y+6=44y−3\frac { 2 y - 10 } { 8 y ^ { 2 } + 18 y - 18 } - \frac { 4 } { 2 y + 6 } = \frac { 4 } { 4 y - 3 }8y2+18y−182y−10​−2y+64​=4y−34​

Perform the indicated division and express your answer in simplest form. 2y2−3y−20(y−4)2÷2y2+13y+202y2−7y−4\frac { 2 y ^ { 2 } - 3 y - 20 } { ( y - 4 ) ^ { 2 } } \div \frac { 2 y ^ { 2 } + 13 y + 20 } { 2 y ^ { 2 } - 7 y - 4 }(y−4)22y2−3y−20​÷2y2−7y−42y2+13y+20​

Simplify the fraction to lowest terms. 3,5001,500\frac { 3,500 } { 1,500 }1,5003,500​

Solve the following equation for the variable x . y=45x+520y = \frac { 4 } { 5 } x + \frac { 5 } { 20 }y=54​x+205​

Solve the following equation for the variable x . y=−lgx+eny = - \frac { l } { g } x + \frac { e } { n }y=−gl​x+ne​

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.)Round your answer to the nearest integer.

Perform the division. −10a2b2−20a2b−15ab2−5ab\frac { - 10 a ^ { 2 } b ^ { 2 } - 20 a ^ { 2 } b - 15 a b ^ { 2 } } { - 5 a b }−5ab−10a2b2−20a2b−15ab2​

Solve for the variable in the proportion. x+24=612\frac { x + 2 } { 4 } = \frac { 6 } { 12 }4x+2​=126​

Find the quotient. 52÷(−37)\frac { 5 } { 2 } \div \left( - \frac { 3 } { 7 } \right)25​÷(−73​)

Multiply and reduce your answer to lowest terms. −425⋅721⋅114- \frac { 42 } { 5 } \cdot \frac { 7 } { 21 } \cdot \frac { 1 } { 14 }−542​⋅217​⋅141​

Solve the equation. 3a−96+4a−44+3a+94=11\frac { 3 a - 9 } { 6 } + \frac { 4 a - 4 } { 4 } + \frac { 3 a + 9 } { 4 } = 1163a−9​+44a−4​+43a+9​=11

Perform the indicated operation and express your answer in simplest form. 6x2−5x−24−1x2−3x−40\frac { 6 } { x ^ { 2 } - 5 x - 24 } - \frac { 1 } { x ^ { 2 } - 3 x - 40 }x2−5x−246​−x2−3x−401​

Solve the following equation for the variable y . −2x−4=3y−1- \frac { 2 } { x - 4 } = \frac { 3 } { y - 1 }−x−42​=y−13​

Solve the equation. 3+12t−7=12t(t−7)3 + \frac { 12 } { t - 7 } = \frac { 12 } { t ( t - 7 ) }3+t−712​=t(t−7)12​

Perform the multiplication. Simplify the answer, if possible. 2z−4z+2⋅55z−10\frac { 2 z - 4 } { z + 2 } \cdot \frac { 5 } { 5 z - 10 }z+22z−4​⋅5z−105​

Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. a = 11, b = 7, c = 31

Perform the operations. 2s2+12s−80s2−16⋅s−2s2−100÷s2−4s2+6s+8\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }s2−162s2+12s−80​⋅s2−100s−2​÷s2+6s+8s2−4​

Simplify the complex fraction. −7x−14x+72x2+7x+2x\frac { - \frac { 7 } { x } - \frac { 14 } { x + 7 } } { \frac { 2 } { x ^ { 2 } + 7 x } + \frac { 2 } { x } }x2+7x2​+x2​−x7​−x+714​​

Perform the indicated operation and express your answer in simplest form. 11x+41x2−9−6x−3\frac { 11 x + 41 } { x ^ { 2 } - 9 } - \frac { 6 } { x - 3 }x2−911x+41​−x−36​

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Solve the equation. $5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }$

Solve the equation. $\frac { 2 y - 10 } { 8 y ^ { 2 } + 18 y - 18 } - \frac { 4 } { 2 y + 6 } = \frac { 4 } { 4 y - 3 }$

Perform the indicated division and express your answer in simplest form. $\frac { 2 y ^ { 2 } - 3 y - 20 } { ( y - 4 ) ^ { 2 } } \div \frac { 2 y ^ { 2 } + 13 y + 20 } { 2 y ^ { 2 } - 7 y - 4 }$

Simplify the fraction to lowest terms. $\frac { 3,500 } { 1,500 }$

Solve the following equation for the variable x . $y = \frac { 4 } { 5 } x + \frac { 5 } { 20 }$

Solve the following equation for the variable x . $y = - \frac { l } { g } x + \frac { e } { n }$

Perform the division. $\frac { - 10 a ^ { 2 } b ^ { 2 } - 20 a ^ { 2 } b - 15 a b ^ { 2 } } { - 5 a b }$

Solve for the variable in the proportion. $\frac { x + 2 } { 4 } = \frac { 6 } { 12 }$

Find the quotient. $\frac { 5 } { 2 } \div \left( - \frac { 3 } { 7 } \right)$

Multiply and reduce your answer to lowest terms. $- \frac { 42 } { 5 } \cdot \frac { 7 } { 21 } \cdot \frac { 1 } { 14 }$

Solve the equation. $\frac { 3 a - 9 } { 6 } + \frac { 4 a - 4 } { 4 } + \frac { 3 a + 9 } { 4 } = 11$

Perform the indicated operation and express your answer in simplest form. $\frac { 6 } { x ^ { 2 } - 5 x - 24 } - \frac { 1 } { x ^ { 2 } - 3 x - 40 }$

Solve the following equation for the variable y . $- \frac { 2 } { x - 4 } = \frac { 3 } { y - 1 }$

Solve the equation. $3 + \frac { 12 } { t - 7 } = \frac { 12 } { t ( t - 7 ) }$

Perform the multiplication. Simplify the answer, if possible. $\frac { 2 z - 4 } { z + 2 } \cdot \frac { 5 } { 5 z - 10 }$

Perform the operations. $\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }$

Simplify the complex fraction. $\frac { - \frac { 7 } { x } - \frac { 14 } { x + 7 } } { \frac { 2 } { x ^ { 2 } + 7 x } + \frac { 2 } { x } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 11 x + 41 } { x ^ { 2 } - 9 } - \frac { 6 } { x - 3 }$