Question 1

Perform the indicated operation. Simplify if possible.
-$\frac { 3 a } { b } + \frac { 3 b } { 2 }$

Accepted Answer

A)  $\frac { 6 a + 3 b } { 2 b }$ 
B)  $\frac { 6 a + 3 b ^ { 2 } } { 2 b }$ 
C)  $6 a + 3 b ^ { 2 }$ 
D)  $\frac { 3 a + 3 b } { 2 b }$ 
A)  $\frac { 6 a + 3 b } { 2 b }$ 
B)  $\frac { 6 a + 3 b ^ { 2 } } { 2 b }$ 
C)  $6 a + 3 b ^ { 2 }$ 
D)  $\frac { 3 a + 3 b } { 2 b }$

Question 2

Perform the indicated operation and simplify if possible.
-$\frac { 7 a } { a ^ { 2 } + 5 a + 4 } - \frac { 2 } { a + 4 }$

Accepted Answer

A)  $\frac { 5 a - 2 } { ( a + 1 ) ( a + 4 ) }$ 
B)  $\frac { 5 a + 2 } { ( a - 1 ) ( a + 4 ) }$ 
C)  $\frac { 5 a - 2 } { ( a - 1 ) ( a + 4 ) }$ 
D)  $\frac { 5 a + 2 } { ( a + 1 ) ( a + 4 ) }$ 
A)  $\frac { 5 a - 2 } { ( a + 1 ) ( a + 4 ) }$ 
B)  $\frac { 5 a + 2 } { ( a - 1 ) ( a + 4 ) }$ 
C)  $\frac { 5 a - 2 } { ( a - 1 ) ( a + 4 ) }$ 
D)  $\frac { 5 a + 2 } { ( a + 1 ) ( a + 4 ) }$

Question 3

Solve the equation.
-$\frac { 2 } { t } = \frac { t } { 5 t - 12 }$

Accepted Answer

A)  0,36 
B)  $0 , \frac { 24 } { 9 }$ 
C)  4,6 
D)  0 
A)  0,36 
B)  $0 , \frac { 24 } { 9 }$ 
C)  4,6 
D)  0

Question 4

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-$\frac { x } { 2 } = \frac { 7 } { 16 }$ is an example of $\mathrm { a } ( \mathrm { n } )$_____

Accepted Answer

A)  complex fraction 
B)  least common denominator 
C)  proportion 
D)  reciprocals 
A)  complex fraction 
B)  least common denominator 
C)  proportion 
D)  reciprocals

Question 5

Find the quotient and simplify.
-$\frac { 33 x - 33 } { 7 } \div \frac { 11 x - 11 } { 70 }$

Accepted Answer

A)  30 
B)  $\frac { 1 } { 30 }$ 
C)  $\frac { 10 ( 33 x - 33 ) } { 11 x - 11 }$ 
D)  $\frac { 363 ( x - 1 ) ^ { 2 } } { 490 }$ 
A)  30 
B)  $\frac { 1 } { 30 }$ 
C)  $\frac { 10 ( 33 x - 33 ) } { 11 x - 11 }$ 
D)  $\frac { 363 ( x - 1 ) ^ { 2 } } { 490 }$

Question 6

Find the quotient and simplify.
-$\frac { 7 x ^ { 9 } } { 9 x ^ { 2 } } \div \frac { 56 x } { 72 x ^ { 4 } }$

Accepted Answer

A)  $x ^ { 10 }$ 
B)  $\frac { 392 x ^ { 4 } } { 648 }$ 
C)  $\frac { 49 x ^ { 4 } } { 81 }$ 
D)  $\frac { 7 x ^ { 10 } } { 9 }$ 
A)  $x ^ { 10 }$ 
B)  $\frac { 392 x ^ { 4 } } { 648 }$ 
C)  $\frac { 49 x ^ { 4 } } { 81 }$ 
D)  $\frac { 7 x ^ { 10 } } { 9 }$

Question 7

Simplify.
-$\frac { 1 - \frac { 2 } { x } } { x - \frac { 4 } { x } }$

Accepted Answer

A)  $x + 2$ 
B)  $\frac { 1 } { x + 2 }$ 
C)  $\frac { 1 } { x - 2 }$ 
D)  $x - 2$ 
A)  $x + 2$ 
B)  $\frac { 1 } { x + 2 }$ 
C)  $\frac { 1 } { x - 2 }$ 
D)  $x - 2$

Question 8

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

Accepted Answer

A)  proportion 
B)  rational expression 
C)  cross products 
D)  complex fraction 
A)  proportion 
B)  rational expression 
C)  cross products 
D)  complex fraction

Question 9

Find the product and simplify.
-$\frac { z ^ { 3 } } { 20 z } \cdot \frac { 4 } { 2 z ^ { 2 } }$

Accepted Answer

A)  $\frac { z } { 10 }$ 
B)  $\frac { 1 } { 10 z }$ 
C)  $\frac { z ^ { 3 } } { 10 z ^ { 2 } }$ 
D)  $\frac { 1 } { 10 }$ 
A)  $\frac { z } { 10 }$ 
B)  $\frac { 1 } { 10 z }$ 
C)  $\frac { z ^ { 3 } } { 10 z ^ { 2 } }$ 
D)  $\frac { 1 } { 10 }$

Question 10

Perform the indicated operations. Simplify if possible.
-$\frac { 3 x } { x ^ { 2 } - 5 x - 36 } - \frac { x - 1 } { x ^ { 2 } - 16 } + \frac { 1 } { x ^ { 2 } - 13 x + 36 }$

Accepted Answer

A)  $\frac { 2 x ^ { 2 } - 21 x + 13 } { ( x - 9 ) ( x + 4 ) ( x - 4 ) }$ 
B)  $\frac { 2 x - 1 } { ( x - 9 ) ( x - 4 ) }$ 
C)  $\frac { 2 x - 1 } { ( x - 9 ) ( x + 4 ) }$ 
D)  $\frac { 2 x ^ { 2 } - x - 5 } { ( x - 9 ) ( x + 4 ) ( x - 4 ) }$ 
A)  $\frac { 2 x ^ { 2 } - 21 x + 13 } { ( x - 9 ) ( x + 4 ) ( x - 4 ) }$ 
B)  $\frac { 2 x - 1 } { ( x - 9 ) ( x - 4 ) }$ 
C)  $\frac { 2 x - 1 } { ( x - 9 ) ( x + 4 ) }$ 
D)  $\frac { 2 x ^ { 2 } - x - 5 } { ( x - 9 ) ( x + 4 ) ( x - 4 ) }$

Question 11

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 an expression that can be written in the form $\frac { \mathrm { P } } { \mathrm { Q } } \text {, where } \mathrm { P } \text { and } \mathrm { Q } \text { are }$ polynomials and Q is not 0.

Accepted Answer

A)  ratio 
B)  rational expression 
C)  proportion 
D)  complex fraction 
A)  ratio 
B)  rational expression 
C)  proportion 
D)  complex fraction

Question 12

Solve.
-Two angles are said to be supplementary if their sum is $180 ^ { \circ }$. If one angle measures $\frac { x - 3 } { x }$ degrees, find the measure of its supplement.

Accepted Answer

A)  $\left( \frac { 179 x + 3 } { x } \right) ^ { \circ }$ 
B)  $\left( \frac { 180 x + 3 } { x } \right) ^ { \circ }$ 
C)  $\left( \frac { 180 x - 3 } { x } \right) ^ { \circ }$ 
D)  $\left( \frac { 179 x - 3 } { x } \right) ^ { \circ }$ 
A)  $\left( \frac { 179 x + 3 } { x } \right) ^ { \circ }$ 
B)  $\left( \frac { 180 x + 3 } { x } \right) ^ { \circ }$ 
C)  $\left( \frac { 180 x - 3 } { x } \right) ^ { \circ }$ 
D)  $\left( \frac { 179 x - 3 } { x } \right) ^ { \circ }$

Question 13

Rewrite the rational expression as an equivalent rational expression with the given denominator.
-$\frac { x } { x + 2 } = \frac { } { 5 x + 10 }$

Accepted Answer

A)  $\frac { x } { 5 x + 10 }$ 
B)  $\frac { 5 x } { 5 x + 10 }$ 
C)  $\frac { 5 } { 5 x + 10 }$ 
D)  $\frac { 2 x } { 5 x + 10 }$ 
A)  $\frac { x } { 5 x + 10 }$ 
B)  $\frac { 5 x } { 5 x + 10 }$ 
C)  $\frac { 5 } { 5 x + 10 }$ 
D)  $\frac { 2 x } { 5 x + 10 }$

Question 14

$$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$$
-$f ( x ) = \frac { 1 } { 3 x }$

Accepted Answer

A)  $\frac { - 1 } { a ( a + h ) }$ 
B)  0 
C)  $\frac { - 1 } { 3 a ( a + h ) }$ 
D)  $\frac { 1 } { 3 a }$ 
A)  $\frac { - 1 } { a ( a + h ) }$ 
B)  0 
C)  $\frac { - 1 } { 3 a ( a + h ) }$ 
D)  $\frac { 1 } { 3 a }$

Question 15

Solve the equation for the indicated variable.
-$A = \frac { h ( a + b ) } { 2 } \quad$ for $a$

Accepted Answer

A)  $a = \frac { h b - 2 A } { h }$ 
B)  $a = \frac { 2 \mathrm { Ab } - \mathrm { h } } { \mathrm { h } }$ 
C)  $a = \frac { 2 \mathrm {~A} - \mathrm { hb } } { \mathrm { h } }$ 
D)  $a = \frac { A - h b } { 2 h }$ 
A)  $a = \frac { h b - 2 A } { h }$ 
B)  $a = \frac { 2 \mathrm { Ab } - \mathrm { h } } { \mathrm { h } }$ 
C)  $a = \frac { 2 \mathrm {~A} - \mathrm { hb } } { \mathrm { h } }$ 
D)  $a = \frac { A - h b } { 2 h }$

Question 16

Perform the indicated operation. Simplify if possible.
-$\frac { 9 } { m + 9 } + \frac { m } { m + 9 }$

Accepted Answer

A)  1 
B)  $\frac { 9 m } { m + 9 }$ 
C)  $\mathrm { m }$ 
D)  9 
A)  1 
B)  $\frac { 9 m } { m + 9 }$ 
C)  $\mathrm { m }$ 
D)  9

Question 17

Simplify the expression.
-$\frac { 3 x + 2 } { 15 x ^ { 2 } + 19 x + 6 }$

Accepted Answer

A)  $\frac { 1 } { 5 x + 3 }$ 
B)  $\frac { 3 x } { 5 x + 3 }$ 
C)  $\frac { 3 x + 2 } { 15 x ^ { 2 } + 19 x + 6 }$ 
D)  $\frac { 3 x + 5 } { 5 x + 19 }$ 
A)  $\frac { 1 } { 5 x + 3 }$ 
B)  $\frac { 3 x } { 5 x + 3 }$ 
C)  $\frac { 3 x + 2 } { 15 x ^ { 2 } + 19 x + 6 }$ 
D)  $\frac { 3 x + 5 } { 5 x + 19 }$

Question 18

Perform the indicated operation. Simplify if possible.
-$\frac { 6 x - 6 } { 5 } \div \frac { 2 x - 2 } { 55 }$

Accepted Answer

A)  33 
B)  $\frac { 12 ( x - 1 ) ^ { 2 } } { 275 }$ 
C)  $\frac { 11 ( 6 x - 6 ) } { 2 x - 2 }$ 
D)  $\frac { 1 } { 33 }$ 
A)  33 
B)  $\frac { 12 ( x - 1 ) ^ { 2 } } { 275 }$ 
C)  $\frac { 11 ( 6 x - 6 ) } { 2 x - 2 }$ 
D)  $\frac { 1 } { 33 }$

Question 19

Solve.
-A recent advertisement claimed that 2 out of every 3 doctors recommend a certain herbal supplement to increase energy levels. If a local hospital employs 250 doctors, how many doctors would you expect to recommend the supplement? (Round to the nearest whole number, if necessary.)

Accepted Answer

A)  375 doctors 
B)  83 doctors 
C)  167 doctors 
D)  1500 doctors 
A)  375 doctors 
B)  83 doctors 
C)  167 doctors 
D)  1500 doctors

Question 20

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

Accepted Answer

A)  $x = 41$ 
B)  $x = 36$ 
C)  $x = 44$ 
D)  $x = 55$ 
A)  $x = 41$ 
B)  $x = 36$ 
C)  $x = 44$ 
D)  $x = 55$

Perform the indicated operation. Simplify if possible. - $\frac { 3 a } { b } + \frac { 3 b } { 2 }$

Perform the indicated operation and simplify if possible. - $\frac { 7 a } { a ^ { 2 } + 5 a + 4 } - \frac { 2 } { a + 4 }$

Solve the equation. - $\frac { 2 } { t } = \frac { t } { 5 t - 12 }$

Find the quotient and simplify. - $\frac { 33 x - 33 } { 7 } \div \frac { 11 x - 11 } { 70 }$

Find the quotient and simplify. - $\frac { 7 x ^ { 9 } } { 9 x ^ { 2 } } \div \frac { 56 x } { 72 x ^ { 4 } }$

Simplify. - $\frac { 1 - \frac { 2 } { x } } { x - \frac { 4 } { x } }$

Find the product and simplify. - $\frac { z ^ { 3 } } { 20 z } \cdot \frac { 4 } { 2 z ^ { 2 } }$

Perform the indicated operations. Simplify if possible. - $\frac { 3 x } { x ^ { 2 } - 5 x - 36 } - \frac { x - 1 } { x ^ { 2 } - 16 } + \frac { 1 } { x ^ { 2 } - 13 x + 36 }$

Solve. -Two angles are said to be supplementary if their sum is $180 ^ { \circ }$ . If one angle measures $\frac { x - 3 } { x }$ degrees, find the measure of its supplement.

Rewrite the rational expression as an equivalent rational expression with the given denominator. - $\frac { x } { x + 2 } = \frac { } { 5 x + 10 }$

$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$ - $f ( x ) = \frac { 1 } { 3 x }$

Solve the equation for the indicated variable. - $A = \frac { h ( a + b ) } { 2 } \quad$ for $a$

Perform the indicated operation. Simplify if possible. - $\frac { 9 } { m + 9 } + \frac { m } { m + 9 }$

Simplify the expression. - $\frac { 3 x + 2 } { 15 x ^ { 2 } + 19 x + 6 }$

Perform the indicated operation. Simplify if possible. - $\frac { 6 x - 6 } { 5 } \div \frac { 2 x - 2 } { 55 }$

Solve. -A recent advertisement claimed that 2 out of every 3 doctors recommend a certain herbal supplement to increase energy levels. If a local hospital employs 250 doctors, how many doctors would you expect to recommend the supplement? (Round to the nearest whole number, if necessary.)

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. - 3ab+3b2\frac { 3 a } { b } + \frac { 3 b } { 2 }b3a​+23b​

Perform the indicated operation and simplify if possible. - 7aa2+5a+4−2a+4\frac { 7 a } { a ^ { 2 } + 5 a + 4 } - \frac { 2 } { a + 4 }a2+5a+47a​−a+42​

Solve the equation. - 2t=t5t−12\frac { 2 } { t } = \frac { t } { 5 t - 12 }t2​=5t−12t​

Find the quotient and simplify. - 33x−337÷11x−1170\frac { 33 x - 33 } { 7 } \div \frac { 11 x - 11 } { 70 }733x−33​÷7011x−11​

Find the quotient and simplify. - 7x99x2÷56x72x4\frac { 7 x ^ { 9 } } { 9 x ^ { 2 } } \div \frac { 56 x } { 72 x ^ { 4 } }9x27x9​÷72x456x​

Simplify. - 1−2xx−4x\frac { 1 - \frac { 2 } { x } } { x - \frac { 4 } { x } }x−x4​1−x2​​

Find the product and simplify. - z320z⋅42z2\frac { z ^ { 3 } } { 20 z } \cdot \frac { 4 } { 2 z ^ { 2 } }20zz3​⋅2z24​

Perform the indicated operations. Simplify if possible. - 3xx2−5x−36−x−1x2−16+1x2−13x+36\frac { 3 x } { x ^ { 2 } - 5 x - 36 } - \frac { x - 1 } { x ^ { 2 } - 16 } + \frac { 1 } { x ^ { 2 } - 13 x + 36 }x2−5x−363x​−x2−16x−1​+x2−13x+361​

Solve. -Two angles are said to be supplementary if their sum is 180∘180 ^ { \circ }180∘ . If one angle measures x−3x\frac { x - 3 } { x }xx−3​ degrees, find the measure of its supplement.

Rewrite the rational expression as an equivalent rational expression with the given denominator. - xx+2=5x+10\frac { x } { x + 2 } = \frac { } { 5 x + 10 }x+2x​=5x+10​

Solve the equation for the indicated variable. - A=h(a+b)2A = \frac { h ( a + b ) } { 2 } \quadA=2h(a+b)​ for aaa

Perform the indicated operation. Simplify if possible. - 9m+9+mm+9\frac { 9 } { m + 9 } + \frac { m } { m + 9 }m+99​+m+9m​

Simplify the expression. - 3x+215x2+19x+6\frac { 3 x + 2 } { 15 x ^ { 2 } + 19 x + 6 }15x2+19x+63x+2​

Perform the indicated operation. Simplify if possible. - 6x−65÷2x−255\frac { 6 x - 6 } { 5 } \div \frac { 2 x - 2 } { 55 }56x−6​÷552x−2​