Question 1

Simplify.
-$\frac{4 x+2}{20 x^{2}+26 x+8}$

Accepted Answer

A)  $\frac{4 x+5}{5 x+26}$ 
B)  $\frac{4 x+2}{20 x^{2}+26 x+8}$ 
C)  $\frac{4 x}{5 x+4}$ 
D)  $\frac{1}{5 x+4}$ 
A)  $\frac{4 x+5}{5 x+26}$ 
B)  $\frac{4 x+2}{20 x^{2}+26 x+8}$ 
C)  $\frac{4 x}{5 x+4}$ 
D)  $\frac{1}{5 x+4}$

Question 2

Find all numbers for which the rational expression is not defined.
-$\frac{2 y-6}{y^{2}-49}$

Accepted Answer

A)  $y=49$ 
B)  $y=7$ 
C)  $y=7$ and $y=-7$ 
D)  $y=3$ 
A)  $y=49$ 
B)  $y=7$ 
C)  $y=7$ and $y=-7$ 
D)  $y=3$

Question 3

In the given problem $\frac{16(\mathrm{y}+9)}{4(\mathrm{y}-7)} \div \frac{?}{(\mathrm{y}-7)(\mathrm{y}-6)}=\frac{4(\mathrm{y}-6)}{(\mathrm{y}-9)}$, what must be the polynomial that is represented by the question mark?

Accepted Answer

A)  $\frac{(y-6) 2(y-7)^{2}}{(y-9)(y+9)}$ 
B)  $(y+9)(y-9)$ 
C)  $\frac{16(y+9)}{(y-9)(y-7)^{2}}$ 
D)  $(y-9)(y-9)$ 
A)  $\frac{(y-6) 2(y-7)^{2}}{(y-9)(y+9)}$ 
B)  $(y+9)(y-9)$ 
C)  $\frac{16(y+9)}{(y-9)(y-7)^{2}}$ 
D)  $(y-9)(y-9)$

Question 4

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=230$, when $x=90$

Accepted Answer

A)  $y=2.56 x$ 
B)  $y=0.39 x$ 
C)  $x=2.56 y$ 
D)  $x=140 y$ 
A)  $y=2.56 x$ 
B)  $y=0.39 x$ 
C)  $x=2.56 y$ 
D)  $x=140 y$

Question 5

Solve the problem.
-The time $T$ necessary to make an enlargement of a photo negative varies directly as the area $A$ of the enlargement. If 120 seconds are required to make a 3-by-5 enlargement, find the time required for a 6 -by-8 enlargement.

Accepted Answer

A)  $336 \mathrm{sec}$ 
B)  $432 \mathrm{sec}$ 
C)  $480 \mathrm{sec}$ 
D)  $384 \mathrm{sec}$ 
A)  $336 \mathrm{sec}$ 
B)  $432 \mathrm{sec}$ 
C)  $480 \mathrm{sec}$ 
D)  $384 \mathrm{sec}$

Question 6

Solve the problem.
-The weight $W$ of an object on the Moon varies directly as the weight $E$ on earth. A person who weighs $168 \mathrm{lb}$ on earth weighs $33.6 \mathrm{lb}$ on the Moon. How much would a 122-lb person weigh on the Moon?

Accepted Answer

A)  $0.2 \mathrm{lb}$ 
B)  $323.6 \mathrm{lb}$ 
C)  $610 \mathrm{lb}$ 
D)  $24.4 \mathrm{lb}$ 
A)  $0.2 \mathrm{lb}$ 
B)  $323.6 \mathrm{lb}$ 
C)  $610 \mathrm{lb}$ 
D)  $24.4 \mathrm{lb}$

Question 7

Find all numbers for which the rational expression is not defined.
-$\frac{x^{2}-81}{x^{2}-2 x-15}$

Accepted Answer

A)  $x=9$ and $x=-9$ 
B)  $x=0$ 
C)  $x=5$ and $x=-3$ 
D)  $x=-5$ and $x=3$ 
A)  $x=9$ and $x=-9$ 
B)  $x=0$ 
C)  $x=5$ and $x=-3$ 
D)  $x=-5$ and $x=3$

Question 8

Solve the problem.
-A quality-control inspector examined 270 calculators and found 11 of them to be defective. At this rate, how many defective calculators will there be in a batch of 15,390 calculators?

Accepted Answer

A)  57 
B)  5 
C)  627 
D)  2970 
A)  57 
B)  5 
C)  627 
D)  2970

Question 9

Find the LCM.
-$t, t-6$

Accepted Answer

A)  12 
B)  $\mathrm{t}$ 
C)  $t-6$ 
D)  $t(t-6)$ 
A)  12 
B)  $\mathrm{t}$ 
C)  $t-6$ 
D)  $t(t-6)$

Question 10

Solve the problem.
-If $x$ varies inversely as $v$, and $x=40$ when $v=4$, find $x$ when $v=32$.

Accepted Answer

A)  $x=20$ 
B)  $x=8$ 
C)  $x=5$ 
D)  $x=16$ 
A)  $x=20$ 
B)  $x=8$ 
C)  $x=5$ 
D)  $x=16$

Question 11

Subtract. Simplify, if possible.
-$\frac{2 x-4}{x^{2}-4}-\frac{2 x-4}{4-x^{2}}$

Accepted Answer

A)  $\frac{4}{x-2}$ 
B)  $\frac{4}{x+2}$ 
C)  4 
D)  0 
A)  $\frac{4}{x-2}$ 
B)  $\frac{4}{x+2}$ 
C)  4 
D)  0

Question 12

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=2.1$, when $x=1.2$

Accepted Answer

A)  $y=\frac{1}{1.75} x$ 
B)  $y=2.1 x$ 
C)  $y=\frac{2.52}{x}$ 
D)  $y=1.75 x$ 
A)  $y=\frac{1}{1.75} x$ 
B)  $y=2.1 x$ 
C)  $y=\frac{2.52}{x}$ 
D)  $y=1.75 x$

Question 13

Find all numbers for which the rational expression is not defined.
-$\frac{b-7}{7 b-28}$

Accepted Answer

A)  $b=4$ 
B)  $b=28$ 
C)  $b=0$ 
D)  $b=-7$ 
A)  $b=4$ 
B)  $b=28$ 
C)  $b=0$ 
D)  $b=-7$

Question 14

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=0.8$, when $x=0.5$

Accepted Answer

A)  $x=0.8 y$ 
B)  $y=1.6 x$ 
C)  $y=0.8 x$ 
D)  $x=1.6 y$ 
A)  $x=0.8 y$ 
B)  $y=1.6 x$ 
C)  $y=0.8 x$ 
D)  $x=1.6 y$

Question 15

Solve the equation.
-$\frac{-8}{x+8}=\frac{x}{x+8}$

Accepted Answer

A)  No solution 
B)  0 
C)  -8 
D)  8 
A)  No solution 
B)  0 
C)  -8 
D)  8

Question 16

Add. Simplify, if possible.
-$\frac{5}{r}+\frac{9}{r-7}$

Accepted Answer

A)  $\frac{14 r-35}{r(7-r)}$ 
B)  $\frac{14 \mathrm{r}-35}{\mathrm{r}(\mathrm{r}-7)}$ 
C)  $\frac{35 r-14}{r(r-7)}$ 
D)  $\frac{35 r-14}{r(7-r)}$ 
A)  $\frac{14 r-35}{r(7-r)}$ 
B)  $\frac{14 \mathrm{r}-35}{\mathrm{r}(\mathrm{r}-7)}$ 
C)  $\frac{35 r-14}{r(r-7)}$ 
D)  $\frac{35 r-14}{r(7-r)}$

Question 17

Solve the problem.
-Tom Quig traveled 280 miles east of St. Louis. For most of the trip he averaged $60 \mathrm{mph}$, but for one period of time he was slowed to $10 \mathrm{mph}$ due to a major accident. If the total time of travel was 8 hours, how many miles did he drive at the reduced speed?

Accepted Answer

A)  40 miles 
B)  50 miles 
C)  35 miles 
D)  60 miles 
A)  40 miles 
B)  50 miles 
C)  35 miles 
D)  60 miles

Question 18

Add. Simplify, if possible.
-$\frac{3}{r}+\frac{4}{r-5}$

Accepted Answer

A)  $\frac{15 r-7}{r(r-5)}$ 
B)  $\frac{7 r-15}{r(5-r)}$ 
C)  $\frac{15 r-7}{r(5-r)}$ 
D)  $\frac{7 r-15}{r(r-5)}$ 
A)  $\frac{15 r-7}{r(r-5)}$ 
B)  $\frac{7 r-15}{r(5-r)}$ 
C)  $\frac{15 r-7}{r(5-r)}$ 
D)  $\frac{7 r-15}{r(r-5)}$

Question 19

Simplify.
-$\frac{y^{2}+3 y-18}{y^{2}+12 y+36}$

Accepted Answer

A)  $\frac{3 y-18}{12 y+36}$ 
B)  $-\frac{y^{2}+3 y-18}{y^{2}+12 y+36}$ 
C)  $\frac{y-3}{y+6}$ 
D)  $\frac{3 y+18}{12 y-12}$ 
A)  $\frac{3 y-18}{12 y+36}$ 
B)  $-\frac{y^{2}+3 y-18}{y^{2}+12 y+36}$ 
C)  $\frac{y-3}{y+6}$ 
D)  $\frac{3 y+18}{12 y-12}$

Question 20

Perform the indicated operation. Simplify, if possible.
-$\frac{4(y-1)}{5 y-2}-\frac{y-4}{2-5 y}-\frac{5 y}{5 y-2}$

Accepted Answer

A)  $\frac{-2 y}{5 y-2}$ 
B)  $\frac{-8}{(5 y-2)(2-5 y)}$ 
C)  $\frac{-8}{5 y-2}$ 
D)  $\frac{8}{5 y-2}$ 
A)  $\frac{-2 y}{5 y-2}$ 
B)  $\frac{-8}{(5 y-2)(2-5 y)}$ 
C)  $\frac{-8}{5 y-2}$ 
D)  $\frac{8}{5 y-2}$

Simplify. - $\frac{4 x+2}{20 x^{2}+26 x+8}$

Find all numbers for which the rational expression is not defined. - $\frac{2 y-6}{y^{2}-49}$

In the given problem $\frac{16(\mathrm{y}+9)}{4(\mathrm{y}-7)} \div \frac{?}{(\mathrm{y}-7)(\mathrm{y}-6)}=\frac{4(\mathrm{y}-6)}{(\mathrm{y}-9)}$ , what must be the polynomial that is represented by the question mark?

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=230$ , when $x=90$

Solve the problem. -The time $T$ necessary to make an enlargement of a photo negative varies directly as the area $A$ of the enlargement. If 120 seconds are required to make a 3-by-5 enlargement, find the time required for a 6 -by-8 enlargement.

Solve the problem. -The weight $W$ of an object on the Moon varies directly as the weight $E$ on earth. A person who weighs $168 \mathrm{lb}$ on earth weighs $33.6 \mathrm{lb}$ on the Moon. How much would a 122-lb person weigh on the Moon?

Find all numbers for which the rational expression is not defined. - $\frac{x^{2}-81}{x^{2}-2 x-15}$

Solve the problem. -A quality-control inspector examined 270 calculators and found 11 of them to be defective. At this rate, how many defective calculators will there be in a batch of 15,390 calculators?

Find the LCM. - $t, t-6$

Solve the problem. -If $x$ varies inversely as $v$ , and $x=40$ when $v=4$ , find $x$ when $v=32$ .

Subtract. Simplify, if possible. - $\frac{2 x-4}{x^{2}-4}-\frac{2 x-4}{4-x^{2}}$

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=2.1$ , when $x=1.2$

Find all numbers for which the rational expression is not defined. - $\frac{b-7}{7 b-28}$

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=0.8$ , when $x=0.5$

Solve the equation. - $\frac{-8}{x+8}=\frac{x}{x+8}$

Add. Simplify, if possible. - $\frac{5}{r}+\frac{9}{r-7}$

Solve the problem. -Tom Quig traveled 280 miles east of St. Louis. For most of the trip he averaged $60 \mathrm{mph}$ , but for one period of time he was slowed to $10 \mathrm{mph}$ due to a major accident. If the total time of travel was 8 hours, how many miles did he drive at the reduced speed?

Add. Simplify, if possible. - $\frac{3}{r}+\frac{4}{r-5}$

Simplify. - $\frac{y^{2}+3 y-18}{y^{2}+12 y+36}$

Perform the indicated operation. Simplify, if possible. - $\frac{4(y-1)}{5 y-2}-\frac{y-4}{2-5 y}-\frac{5 y}{5 y-2}$

Whole Numbers

Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Converting Units of Measurement

Filters

Exam 12: Rational Expressions and Equations

Simplify. - 4x+220x2+26x+8\frac{4 x+2}{20 x^{2}+26 x+8}20x2+26x+84x+2​

Find all numbers for which the rational expression is not defined. - 2y−6y2−49\frac{2 y-6}{y^{2}-49}y2−492y−6​

Given the values of xxx and yyy , find an equation of variation in which yyy varies directly as xxx . - y=230y=230y=230 , when x=90x=90x=90

Solve the problem. -The time TTT necessary to make an enlargement of a photo negative varies directly as the area AAA of the enlargement. If 120 seconds are required to make a 3-by-5 enlargement, find the time required for a 6 -by-8 enlargement.

Solve the problem. -The weight WWW of an object on the Moon varies directly as the weight EEE on earth. A person who weighs 168lb168 \mathrm{lb}168lb on earth weighs 33.6lb33.6 \mathrm{lb}33.6lb on the Moon. How much would a 122-lb person weigh on the Moon?

Find all numbers for which the rational expression is not defined. - x2−81x2−2x−15\frac{x^{2}-81}{x^{2}-2 x-15}x2−2x−15x2−81​