Question 1

Perform the indicated operation. Simplify if possible.
-$\frac { x ^ { 2 } - 10 x + 25 } { 6 x - 30 } \div \frac { 4 x - 20 } { 24 }$

Accepted Answer

A)  24 
B)  1 
C)  $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 36 }$ 
A)  24 
B)  1 
C)  $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 36 }$

Question 2

Perform the indicated operation. Simplify if possible.
-$\frac { 3 x } { x ^ { 2 } - 8 x + 15 } - \frac { 9 } { x ^ { 2 } - 8 x + 15 }$

Accepted Answer

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

Question 3

Perform the indicated operation. Simplify if possible.
-$\frac { 3 m } { 10 n } + \frac { 3 m } { 10 n }$

Accepted Answer

A)  $3 \mathrm {~m}$ 
B)  $\frac { 3 m } { 2 n }$ 
C)  $\frac { 3 m } { 5 n }$ 
D)  $\frac { 5 n } { 3 m }$ 
A)  $3 \mathrm {~m}$ 
B)  $\frac { 3 m } { 2 n }$ 
C)  $\frac { 3 m } { 5 n }$ 
D)  $\frac { 5 n } { 3 m }$

Question 4

Perform the indicated operation. Simplify if possible.
-$\frac { 3 x - 7 } { x ^ { 2 } - 4 x - 12 } - \frac { 2 x - 9 } { x ^ { 2 } - 4 x - 12 }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } - 4 x - 12 }$ 
B)  $\frac { x - 2 } { x ^ { 2 } - 4 x - 12 }$ 
C)  $\frac { 1 } { x - 6 }$ 
D)  $\frac { 1 } { x + 2 }$ 
A)  $\frac { 1 } { x ^ { 2 } - 4 x - 12 }$ 
B)  $\frac { x - 2 } { x ^ { 2 } - 4 x - 12 }$ 
C)  $\frac { 1 } { x - 6 }$ 
D)  $\frac { 1 } { x + 2 }$

Question 5

Simplify.
-$\frac { x ^ { - 2 } } { x ^ { - 2 } - y ^ { - 2 } }$

Accepted Answer

A)  $\frac { y ^ { 2 } - x ^ { 2 } } { y ^ { 2 } }$ 
B)  $\frac { y } { y ^ { 2 } - x ^ { 2 } }$ 
C)  $\frac { y ^ { 2 } } { y ^ { 2 } - x ^ { 2 } }$ 
D)  $\frac { y ^ { 2 } } { y ^ { 2 } + x ^ { 2 } }$ 
A)  $\frac { y ^ { 2 } - x ^ { 2 } } { y ^ { 2 } }$ 
B)  $\frac { y } { y ^ { 2 } - x ^ { 2 } }$ 
C)  $\frac { y ^ { 2 } } { y ^ { 2 } - x ^ { 2 } }$ 
D)  $\frac { y ^ { 2 } } { y ^ { 2 } + x ^ { 2 } }$

Question 6

Simplify.
-$\frac { \frac { 1 } { x } + \frac { 5 } { x ^ { 2 } } } { x + \frac { 125 } { x ^ { 2 } } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } - 5 x + 25 }$ 
B)  $\frac { x + 5 } { x ^ { 3 } + 125 }$ 
C)  $\frac { 1 } { x ^ { 2 } + 5 x + 25 }$ 
D)  $\frac { x + 5 } { x ^ { 2 } + 125 }$ 
A)  $\frac { 1 } { x ^ { 2 } - 5 x + 25 }$ 
B)  $\frac { x + 5 } { x ^ { 3 } + 125 }$ 
C)  $\frac { 1 } { x ^ { 2 } + 5 x + 25 }$ 
D)  $\frac { x + 5 } { x ^ { 2 } + 125 }$

Question 7

Perform the indicated operation. Simplify if possible.
-$\frac { x } { 3 x - 7 } - \frac { 7 } { 27 x - 63 }$

Accepted Answer

A)  $\frac { 9 x - 7 } { 3 x - 7 }$ 
B)  $\frac { 27 x - 189 } { 9 ( 3 x - 7 ) }$ 
C)  $\frac { 9 x - 7 } { 9 ( 3 x - 7 ) }$ 
D)  $\frac { x - 7 } { 9 ( 3 x - 7 ) }$ 
A)  $\frac { 9 x - 7 } { 3 x - 7 }$ 
B)  $\frac { 27 x - 189 } { 9 ( 3 x - 7 ) }$ 
C)  $\frac { 9 x - 7 } { 9 ( 3 x - 7 ) }$ 
D)  $\frac { x - 7 } { 9 ( 3 x - 7 ) }$

Question 8

Rewrite the rational expression as an equivalent rational expression with the given denominator.
-$\frac { 7 } { 8 - y } = \frac { } { y - 8 }$

Accepted Answer

A)  $- \frac { 7 } { y - 8 }$ 
B)  $\frac { 7 } { y - 8 }$ 
C)  $- \frac { 7 ( y - 8 ) } { y - 8 }$ 
D)  $- \frac { 1 } { y - 8 }$ 
A)  $- \frac { 7 } { y - 8 }$ 
B)  $\frac { 7 } { y - 8 }$ 
C)  $- \frac { 7 ( y - 8 ) } { y - 8 }$ 
D)  $- \frac { 1 } { y - 8 }$

Question 9

Perform the indicated operation. Simplify if possible.
-$\frac { x ^ { 2 } - 7 x } { x - 3 } + \frac { 12 } { x - 3 }$

Accepted Answer

A)  $x - 4$ 
B)  $x - 3$ 
C)  $\frac { x ^ { 2 } - 7 x + 12 } { x - 3 }$ 
D)  $x + 4$ 
A)  $x - 4$ 
B)  $x - 3$ 
C)  $\frac { x ^ { 2 } - 7 x + 12 } { x - 3 }$ 
D)  $x + 4$

Question 10

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-A(n) is the quotient of two numbers.

Accepted Answer

A)  least common denominator 
B)  ratio 
C)  denominator 
D)  numerator 
A)  least common denominator 
B)  ratio 
C)  denominator 
D)  numerator

Question 11

Solve.
-In a sample of 75 fluorescent bulbs, 3 were found to be defective. At this rate, how many defective bulbs should be found in 525 bulbs?

Accepted Answer

A)  23 
B)  20 
C)  22 
D)  21 
A)  23 
B)  20 
C)  22 
D)  21

Question 12

Simplify the expression.
-$\frac { y ^ { 2 } + 4 y + 4 } { y ^ { 2 } + 5 y + 6 }$

Accepted Answer

A)  $\frac { 4 y + 4 } { 5 y + 6 }$ 
B)  $\frac { y + 2 } { y + 3 }$ 
C)  $- \frac { y ^ { 2 } + 4 y + 4 } { y ^ { 2 } + 5 y + 6 }$ 
D)  $\frac { 4 y + 2 } { 5 y + 3 }$ 
A)  $\frac { 4 y + 4 } { 5 y + 6 }$ 
B)  $\frac { y + 2 } { y + 3 }$ 
C)  $- \frac { y ^ { 2 } + 4 y + 4 } { y ^ { 2 } + 5 y + 6 }$ 
D)  $\frac { 4 y + 2 } { 5 y + 3 }$

Question 13

Convert as indicated.
-40 miles per hour =_____feet per second (Round to the nearest whole, if necessary.)

Accepted Answer

A)  $\frac { 1 } { 90 }$ 
B)  3520 
C)  211,200 
D)  59 
A)  $\frac { 1 } { 90 }$ 
B)  3520 
C)  211,200 
D)  59

Question 14

Solve.
-Two angles are complementary if the sum of their measures is $90 ^ { \circ }$. If the measure of one angle is given by $\left( \frac { 720 } { y } \right) ^ { \circ }$ and the measure of its complement is given by $\left( \frac { 810 } { y } \right) ^ { \circ }$, find the measures of the two angles.

Accepted Answer

A)  $\frac { 1440 } { 17 } \circ \frac { 1620 } { 17 } \circ$ 
B)  $\frac { 720 } { 17 } \circ \frac { 810 } { 17 }$ 。 
C)  $\left( \frac { 17 } { 2 } \right) ^ { \circ } , \left( \frac { 163 } { 2 } \right) ^ { \circ }$ 
D)  $17 ^ { \circ } , 73 ^ { \circ }$ 
A)  $\frac { 1440 } { 17 } \circ \frac { 1620 } { 17 } \circ$ 
B)  $\frac { 720 } { 17 } \circ \frac { 810 } { 17 }$ 。 
C)  $\left( \frac { 17 } { 2 } \right) ^ { \circ } , \left( \frac { 163 } { 2 } \right) ^ { \circ }$ 
D)  $17 ^ { \circ } , 73 ^ { \circ }$

Question 15

Perform the indicated operation and simplify if possible.
-$\frac { 2 x } { x - 4 } - \frac { x + 3 } { x - 4 }$

Accepted Answer

A)  $\frac { x + 3 } { x - 4 }$ 
B)  $\frac { x - 3 } { x - 4 }$ 
C)  $\frac { 3 x + 3 } { x - 4 }$ 
D)  $\frac { 3 x - 3 } { x - 4 }$ 
A)  $\frac { x + 3 } { x - 4 }$ 
B)  $\frac { x - 3 } { x - 4 }$ 
C)  $\frac { 3 x + 3 } { x - 4 }$ 
D)  $\frac { 3 x - 3 } { x - 4 }$

Question 16

Solve the equation.
-$\frac { x + 3 } { 4 } = \frac { x + 4 } { 5 }$

Accepted Answer

A)  1 
B)  $\frac { 7 } { 20 }$ 
C)  $\frac { 7 } { 9 }$ 
D)  $\frac { 1 } { 20 }$ 
A)  1 
B)  $\frac { 7 } { 20 }$ 
C)  $\frac { 7 } { 9 }$ 
D)  $\frac { 1 } { 20 }$

Question 17

Solve the equation for the indicated variable.
-$\frac { 1 } { a } + \frac { 1 } { b } = c \quad$ for $a$

Accepted Answer

A)  $a = b c - \frac { 1 } { b }$ 
B)  $a = \frac { 1 } { c } - b$ 
C)  $a = \frac { 1 } { b c }$ 
D)  $a = \frac { b } { b c - 1 }$ 
A)  $a = b c - \frac { 1 } { b }$ 
B)  $a = \frac { 1 } { c } - b$ 
C)  $a = \frac { 1 } { b c }$ 
D)  $a = \frac { b } { b c - 1 }$

Question 18

Find the domain of the rational expression.
-$f ( x ) = \frac { 36 x ^ { 2 } - 81 } { 7 x - 35 }$

Accepted Answer

A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\{ x \mid x$ is a real number and $x \neq 5 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 35 \}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 3 } { 2 } , x \neq - \frac { 3 } { 2 } \right\}$ 
A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\{ x \mid x$ is a real number and $x \neq 5 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 35 \}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 3 } { 2 } , x \neq - \frac { 3 } { 2 } \right\}$

Question 19

Simplify.
-$\frac { \frac { 1 } { x } + \frac { 7 } { x ^ { 2 } } } { x + \frac { 343 } { x ^ { 2 } } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } + 7 x + 49 }$ 
B)  $\frac { x + 7 } { x ^ { 2 } + 343 }$ 
C)  $\frac { 1 } { x ^ { 2 } - 7 x + 49 }$ 
D)  $\frac { x + 7 } { x ^ { 3 } + 343 }$ 
A)  $\frac { 1 } { x ^ { 2 } + 7 x + 49 }$ 
B)  $\frac { x + 7 } { x ^ { 2 } + 343 }$ 
C)  $\frac { 1 } { x ^ { 2 } - 7 x + 49 }$ 
D)  $\frac { x + 7 } { x ^ { 3 } + 343 }$

Question 20

Given that the pair of triangles is similar, find the missing length.
-

Accepted Answer

A)  X=32 
B)  X=30 
C)  X=24 
D)  X=40 
A)  X=32 
B)  X=30 
C)  X=24 
D)  X=40

Perform the indicated operation. Simplify if possible. - $\frac { x ^ { 2 } - 10 x + 25 } { 6 x - 30 } \div \frac { 4 x - 20 } { 24 }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 x } { x ^ { 2 } - 8 x + 15 } - \frac { 9 } { x ^ { 2 } - 8 x + 15 }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 m } { 10 n } + \frac { 3 m } { 10 n }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 x - 7 } { x ^ { 2 } - 4 x - 12 } - \frac { 2 x - 9 } { x ^ { 2 } - 4 x - 12 }$

Simplify. - $\frac { x ^ { - 2 } } { x ^ { - 2 } - y ^ { - 2 } }$

Simplify. - $\frac { \frac { 1 } { x } + \frac { 5 } { x ^ { 2 } } } { x + \frac { 125 } { x ^ { 2 } } }$

Perform the indicated operation. Simplify if possible. - $\frac { x } { 3 x - 7 } - \frac { 7 } { 27 x - 63 }$

Rewrite the rational expression as an equivalent rational expression with the given denominator. - $\frac { 7 } { 8 - y } = \frac { } { y - 8 }$

Perform the indicated operation. Simplify if possible. - $\frac { x ^ { 2 } - 7 x } { x - 3 } + \frac { 12 } { x - 3 }$

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. least common denominator simplifying reciprocals numerator cross products ratio proportion denominator rational expression domain complex fraction -A(n) is the quotient of two numbers.

Solve. -In a sample of 75 fluorescent bulbs, 3 were found to be defective. At this rate, how many defective bulbs should be found in 525 bulbs?

Simplify the expression. - $\frac { y ^ { 2 } + 4 y + 4 } { y ^ { 2 } + 5 y + 6 }$

Convert as indicated. -40 miles per hour =_____feet per second (Round to the nearest whole, if necessary.)

Perform the indicated operation and simplify if possible. - $\frac { 2 x } { x - 4 } - \frac { x + 3 } { x - 4 }$

Solve the equation. - $\frac { x + 3 } { 4 } = \frac { x + 4 } { 5 }$

Solve the equation for the indicated variable. - $\frac { 1 } { a } + \frac { 1 } { b } = c \quad$ for $a$

Find the domain of the rational expression. - $f ( x ) = \frac { 36 x ^ { 2 } - 81 } { 7 x - 35 }$

Simplify. - $\frac { \frac { 1 } { x } + \frac { 7 } { x ^ { 2 } } } { x + \frac { 343 } { x ^ { 2 } } }$

Given that the pair of triangles is similar, find the missing length. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Rational Expressions

Perform the indicated operation. Simplify if possible. - x2−10x+256x−30÷4x−2024\frac { x ^ { 2 } - 10 x + 25 } { 6 x - 30 } \div \frac { 4 x - 20 } { 24 }6x−30x2−10x+25​÷244x−20​

Perform the indicated operation. Simplify if possible. - 3xx2−8x+15−9x2−8x+15\frac { 3 x } { x ^ { 2 } - 8 x + 15 } - \frac { 9 } { x ^ { 2 } - 8 x + 15 }x2−8x+153x​−x2−8x+159​

Perform the indicated operation. Simplify if possible. - 3m10n+3m10n\frac { 3 m } { 10 n } + \frac { 3 m } { 10 n }10n3m​+10n3m​

Perform the indicated operation. Simplify if possible. - 3x−7x2−4x−12−2x−9x2−4x−12\frac { 3 x - 7 } { x ^ { 2 } - 4 x - 12 } - \frac { 2 x - 9 } { x ^ { 2 } - 4 x - 12 }x2−4x−123x−7​−x2−4x−122x−9​

Simplify. - x−2x−2−y−2\frac { x ^ { - 2 } } { x ^ { - 2 } - y ^ { - 2 } }x−2−y−2x−2​

Simplify. - 1x+5x2x+125x2\frac { \frac { 1 } { x } + \frac { 5 } { x ^ { 2 } } } { x + \frac { 125 } { x ^ { 2 } } }x+x2125​x1​+x25​​

Perform the indicated operation. Simplify if possible. - x3x−7−727x−63\frac { x } { 3 x - 7 } - \frac { 7 } { 27 x - 63 }3x−7x​−27x−637​

Rewrite the rational expression as an equivalent rational expression with the given denominator. - 78−y=y−8\frac { 7 } { 8 - y } = \frac { } { y - 8 }8−y7​=y−8​

Perform the indicated operation. Simplify if possible. - x2−7xx−3+12x−3\frac { x ^ { 2 } - 7 x } { x - 3 } + \frac { 12 } { x - 3 }x−3x2−7x​+x−312​