Question 1

Simplify.
-$\frac{\frac{1}{m}+\frac{1}{z}}{\frac{1}{m}-\frac{1}{z}}$

Accepted Answer

A)  $\frac{z-m}{z}$ 
B)  $\frac{z+m}{z}$ 
C)  $\frac{z+m}{m}$ 
D)  $\frac{z+m}{z-m}$ 
A)  $\frac{z-m}{z}$ 
B)  $\frac{z+m}{z}$ 
C)  $\frac{z+m}{m}$ 
D)  $\frac{z+m}{z-m}$

Question 2

Find the LCM.
-$x^{2}+4 x+3,-6 x-6$

Accepted Answer

A)  $-6(x-3)(x-1)$ 
B)  $-6(x-3)(x+1)$ 
C)  $-6(x+3)(x+1)$ 
D)  $-6(x+3)(x-1)$ 
A)  $-6(x-3)(x-1)$ 
B)  $-6(x-3)(x+1)$ 
C)  $-6(x+3)(x+1)$ 
D)  $-6(x+3)(x-1)$

Question 3

Subtract. Simplify, if possible.
-$\frac{3}{6 x-7}-\frac{2}{7-6 x}$

Accepted Answer

A)  $\frac{-1}{6 x-7}$ 
B)  $\frac{1}{6 x-7}$ 
C)  $\frac{5}{6 x-7}$ 
D)  $\frac{-5}{6 x-7}$ 
A)  $\frac{-1}{6 x-7}$ 
B)  $\frac{1}{6 x-7}$ 
C)  $\frac{5}{6 x-7}$ 
D)  $\frac{-5}{6 x-7}$

Question 4

Solve the equation.
-$\frac{x}{5}-\frac{5}{x}=0$

Accepted Answer

A)  5 
B)  $-5,0,5$ 
C)  $-5,5$ 
D)  No solution 
A)  5 
B)  $-5,0,5$ 
C)  $-5,5$ 
D)  No solution

Question 5

Subtract. Simplify, if possible.
-$\frac{3 x-5}{4 x^{4}}-\frac{8 x-2}{16 x}$

Accepted Answer

A)  $\frac{-2 x^{4}+0.5 x^{3}+3 x-5}{4 x^{4}}$ 
B)  $\frac{-8 x^{5}+2 x^{4}+12 x^{2}-20 x}{16 x^{5}}$ 
C)  $\frac{-8 x^{4}+2 x^{3}+12 x-20}{16 x^{4}}$ 
D)  $\frac{-5 x-3}{16 x^{4}}$ 
A)  $\frac{-2 x^{4}+0.5 x^{3}+3 x-5}{4 x^{4}}$ 
B)  $\frac{-8 x^{5}+2 x^{4}+12 x^{2}-20 x}{16 x^{5}}$ 
C)  $\frac{-8 x^{4}+2 x^{3}+12 x-20}{16 x^{4}}$ 
D)  $\frac{-5 x-3}{16 x^{4}}$

Question 6

Simplify.
-$\frac{24 k^{3}}{6 k}$

Accepted Answer

A)  18 
B)  $4 \mathrm{k}^{2}$ 
C)  $18 \mathrm{k}^{2}$ 
D)  $4 \mathrm{k}$ 
A)  18 
B)  $4 \mathrm{k}^{2}$ 
C)  $18 \mathrm{k}^{2}$ 
D)  $4 \mathrm{k}$

Question 7

Multiply and, if possible, simplify.
-$\frac{2 z^{3}}{3} \cdot \frac{9}{z^{2}}$

Accepted Answer

A)  $\frac{6}{z}$ 
B)  $6 z$ 
C)  $\frac{6 z^{2}}{z^{3}}$ 
D)  $\frac{z}{6}$ 
A)  $\frac{6}{z}$ 
B)  $6 z$ 
C)  $\frac{6 z^{2}}{z^{3}}$ 
D)  $\frac{z}{6}$

Question 8

Multiply. Do not simplify.
-$\frac{7 y^{4}}{7 y^{4}} \cdot \frac{2 z}{7 x}$

Accepted Answer

A)  $\frac{2 z}{\left(7 y^{4}\right)(7 x)}$ 
B)  $\frac{\left(7 y^{4}\right)(7 x)}{\left(7 y^{4}\right)(2 z)}$ 
C)  $\frac{\left(7 y^{4}\right)(2 z)}{7 x}$ 
D)  $\frac{\left(7 y^{4}\right)(2 z)}{\left(7 y^{4}\right)(7 x)}$ 
A)  $\frac{2 z}{\left(7 y^{4}\right)(7 x)}$ 
B)  $\frac{\left(7 y^{4}\right)(7 x)}{\left(7 y^{4}\right)(2 z)}$ 
C)  $\frac{\left(7 y^{4}\right)(2 z)}{7 x}$ 
D)  $\frac{\left(7 y^{4}\right)(2 z)}{\left(7 y^{4}\right)(7 x)}$

Question 9

Find all numbers for which the rational expression is not defined.
-$\frac{7}{b+8}$

Accepted Answer

A)  $b=0$ 
B)  $b=-8$ 
C)  $b=8$ 
D)  None 
A)  $b=0$ 
B)  $b=-8$ 
C)  $b=8$ 
D)  None

Question 10

Solve the equation.
-$\frac{x}{3}-\frac{x}{9}=7$

Accepted Answer

A)  21 
B)  27 
C)  63 
D)  $\frac{63}{2}$ 
A)  21 
B)  27 
C)  63 
D)  $\frac{63}{2}$

Question 11

Simplify.
-$\frac{\frac{1}{a}+1}{\frac{1}{a}-1}$

Accepted Answer

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

Question 12

Find all numbers for which the rational expression is not defined.
-$\frac{x^{2}-81}{x^{2}+5 x-14}$

Accepted Answer

A)  $x=7$ and $x=-2$ 
B)  $x=0$ 
C)  $x=9$ and $x=-9$ 
D)  $x=-7$ and $x=2$ 
A)  $x=7$ and $x=-2$ 
B)  $x=0$ 
C)  $x=9$ and $x=-9$ 
D)  $x=-7$ and $x=2$

Question 13

Find the reciprocal.
-$\frac{12}{x^{2}+y^{2}}$

Accepted Answer

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

Question 14

Add, first finding the LCD. Simplify, if possible.
-$\frac{10}{13}+\frac{1}{8}$

Accepted Answer

A)  $\frac{11}{21}$ 
B)  $\frac{93}{104}$ 
C)  $\frac{11}{104}$ 
D)  $\frac{31}{7}$ 
A)  $\frac{11}{21}$ 
B)  $\frac{93}{104}$ 
C)  $\frac{11}{104}$ 
D)  $\frac{31}{7}$

Question 15

Solve the equation.
-$\frac{y+1}{y+6}-\frac{y}{y^{2}-36}=\frac{y-3}{y-6}$

Accepted Answer

A)  $\frac{4}{3}$ 
B)  $\frac{4}{5}$ 
C)  1 
D)  $\frac{3}{4}$ 
A)  $\frac{4}{3}$ 
B)  $\frac{4}{5}$ 
C)  1 
D)  $\frac{3}{4}$

Question 16

Solve the problem.
-The distance a vehicle can travel at a fixed speed varies directly as time. If a vehicle travels 900 miles in 15 minutes, how far will it travel in 10 minutes?

Accepted Answer

A)  600 miles 
B)  $\frac{2}{5}$ miles 
C)  40 miles 
D)  $\frac{5}{2}$ miles 
A)  600 miles 
B)  $\frac{2}{5}$ miles 
C)  40 miles 
D)  $\frac{5}{2}$ miles

Question 17

Perform the indicated operation. Simplify, if possible.
-$\frac{\mathrm{b}}{\mathrm{b}^{2}-25}+\frac{5}{\mathrm{~b}+5}-\frac{6}{\mathrm{~b}}$

Accepted Answer

A)  $\frac{6 b^{2}-25 b+150}{b(b+5)(b-5)}$ 
B)  $\frac{-25(b-6)}{b(b+5)(b-5)}$ 
C)  $\frac{25(b+6)}{b(b+5)(b-5)}$ 
D)  $\frac{25(b-6)}{(b+5)(b-5)}$ 
A)  $\frac{6 b^{2}-25 b+150}{b(b+5)(b-5)}$ 
B)  $\frac{-25(b-6)}{b(b+5)(b-5)}$ 
C)  $\frac{25(b+6)}{b(b+5)(b-5)}$ 
D)  $\frac{25(b-6)}{(b+5)(b-5)}$

Question 18

Perform the indicated operation. Simplify, if possible.
-$\frac{-25 x}{7(5 x+1)}+\frac{1}{7 x(5 x+1)}-\frac{3}{x}$

Accepted Answer

A)  $-\frac{5(x+4)}{35 x^{2}+7 x}$ 
B)  $\frac{-25 x^{2}-105 x-20}{35 x^{2}+7 x}$ 
C)  $\frac{-25 x^{2}-105 x-20}{7 x}$ 
D)  $-\frac{5(x+4)}{7 x}$ 
A)  $-\frac{5(x+4)}{35 x^{2}+7 x}$ 
B)  $\frac{-25 x^{2}-105 x-20}{35 x^{2}+7 x}$ 
C)  $\frac{-25 x^{2}-105 x-20}{7 x}$ 
D)  $-\frac{5(x+4)}{7 x}$

Question 19

Subtract. Simplify, if possible.
-$\frac{5}{6-y}-\frac{7}{y-6}$

Accepted Answer

A)  $\frac{12}{6-y}$ 
B)  $\frac{2}{6-y}$ 
C)  $\frac{35}{6-y}$ 
D)  $\frac{-2}{6-y}$ 
A)  $\frac{12}{6-y}$ 
B)  $\frac{2}{6-y}$ 
C)  $\frac{35}{6-y}$ 
D)  $\frac{-2}{6-y}$

Question 20

Add, first finding the LCD. Simplify, if possible.
-$\frac{1}{4}+\frac{2}{7}+\frac{1}{3}$

Accepted Answer

A)  $\frac{2}{7}$ 
B)  $\frac{1}{21}$ 
C)  $\frac{73}{14}$ 
D)  $\frac{73}{84}$ 
A)  $\frac{2}{7}$ 
B)  $\frac{1}{21}$ 
C)  $\frac{73}{14}$ 
D)  $\frac{73}{84}$

Simplify. - $\frac{\frac{1}{m}+\frac{1}{z}}{\frac{1}{m}-\frac{1}{z}}$

Find the LCM. - $x^{2}+4 x+3,-6 x-6$

Subtract. Simplify, if possible. - $\frac{3}{6 x-7}-\frac{2}{7-6 x}$

Solve the equation. - $\frac{x}{5}-\frac{5}{x}=0$

Subtract. Simplify, if possible. - $\frac{3 x-5}{4 x^{4}}-\frac{8 x-2}{16 x}$

Simplify. - $\frac{24 k^{3}}{6 k}$

Multiply and, if possible, simplify. - $\frac{2 z^{3}}{3} \cdot \frac{9}{z^{2}}$

Multiply. Do not simplify. - $\frac{7 y^{4}}{7 y^{4}} \cdot \frac{2 z}{7 x}$

Find all numbers for which the rational expression is not defined. - $\frac{7}{b+8}$

Solve the equation. - $\frac{x}{3}-\frac{x}{9}=7$

Simplify. - $\frac{\frac{1}{a}+1}{\frac{1}{a}-1}$

Find all numbers for which the rational expression is not defined. - $\frac{x^{2}-81}{x^{2}+5 x-14}$

Find the reciprocal. - $\frac{12}{x^{2}+y^{2}}$

Add, first finding the LCD. Simplify, if possible. - $\frac{10}{13}+\frac{1}{8}$

Solve the equation. - $\frac{y+1}{y+6}-\frac{y}{y^{2}-36}=\frac{y-3}{y-6}$

Solve the problem. -The distance a vehicle can travel at a fixed speed varies directly as time. If a vehicle travels 900 miles in 15 minutes, how far will it travel in 10 minutes?

Perform the indicated operation. Simplify, if possible. - $\frac{\mathrm{b}}{\mathrm{b}^{2}-25}+\frac{5}{\mathrm{~b}+5}-\frac{6}{\mathrm{~b}}$

Perform the indicated operation. Simplify, if possible. - $\frac{-25 x}{7(5 x+1)}+\frac{1}{7 x(5 x+1)}-\frac{3}{x}$

Subtract. Simplify, if possible. - $\frac{5}{6-y}-\frac{7}{y-6}$

Add, first finding the LCD. Simplify, if possible. - $\frac{1}{4}+\frac{2}{7}+\frac{1}{3}$

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. - 1m+1z1m−1z\frac{\frac{1}{m}+\frac{1}{z}}{\frac{1}{m}-\frac{1}{z}}m1​−z1​m1​+z1​​

Find the LCM. - x2+4x+3,−6x−6x^{2}+4 x+3,-6 x-6x2+4x+3,−6x−6

Subtract. Simplify, if possible. - 36x−7−27−6x\frac{3}{6 x-7}-\frac{2}{7-6 x}6x−73​−7−6x2​

Solve the equation. - x5−5x=0\frac{x}{5}-\frac{5}{x}=05x​−x5​=0

Subtract. Simplify, if possible. - 3x−54x4−8x−216x\frac{3 x-5}{4 x^{4}}-\frac{8 x-2}{16 x}4x43x−5​−16x8x−2​

Simplify. - 24k36k\frac{24 k^{3}}{6 k}6k24k3​

Multiply and, if possible, simplify. - 2z33⋅9z2\frac{2 z^{3}}{3} \cdot \frac{9}{z^{2}}32z3​⋅z29​

Multiply. Do not simplify. - 7y47y4⋅2z7x\frac{7 y^{4}}{7 y^{4}} \cdot \frac{2 z}{7 x}7y47y4​⋅7x2z​

Find all numbers for which the rational expression is not defined. - 7b+8\frac{7}{b+8}b+87​

Solve the equation. - x3−x9=7\frac{x}{3}-\frac{x}{9}=73x​−9x​=7

Simplify. - 1a+11a−1\frac{\frac{1}{a}+1}{\frac{1}{a}-1}a1​−1a1​+1​

Find all numbers for which the rational expression is not defined. - x2−81x2+5x−14\frac{x^{2}-81}{x^{2}+5 x-14}x2+5x−14x2−81​

Find the reciprocal. - 12x2+y2\frac{12}{x^{2}+y^{2}}x2+y212​

Add, first finding the LCD. Simplify, if possible. - 1013+18\frac{10}{13}+\frac{1}{8}1310​+81​

Solve the equation. - y+1y+6−yy2−36=y−3y−6\frac{y+1}{y+6}-\frac{y}{y^{2}-36}=\frac{y-3}{y-6}y+6y+1​−y2−36y​=y−6y−3​