Question 1

Simplify.
-$\frac{\frac{x}{5 y}-\frac{2}{10 y^{3}}}{\frac{2}{10 y^{3}}-\frac{x}{5 y}}$

Accepted Answer

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

Question 2

Solve the equation.
-$\frac{1}{\mathrm{x}-4}+\frac{1}{2 \mathrm{x}-8}=\frac{3}{2}$

Accepted Answer

A)  5 
B)  15 
C)  1 
D)  -3 
A)  5 
B)  15 
C)  1 
D)  -3

Question 3

Multiply. Do not simplify.
-$\frac{7 a+1}{5 a-1} \cdot \frac{a}{a}$

Accepted Answer

A)  $\frac{(7 a+1) a}{5 a-1}$ 
B)  $\frac{(7 a+1) a}{(5 a-1) a}$ 
C)  $\frac{7 a+1}{(5 a-1) a}$ 
D)  $\frac{(5 a-1) a}{(7 a+1) a}$ 
A)  $\frac{(7 a+1) a}{5 a-1}$ 
B)  $\frac{(7 a+1) a}{(5 a-1) a}$ 
C)  $\frac{7 a+1}{(5 a-1) a}$ 
D)  $\frac{(5 a-1) a}{(7 a+1) a}$

Question 4

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=80$, when $x=260$

Accepted Answer

A)  $y=80 x$ 
B)  $y=0.41 x$ 
C)  $y=0.31 x$ 
D)  $y=3.25 x$ 
A)  $y=80 x$ 
B)  $y=0.41 x$ 
C)  $y=0.31 x$ 
D)  $y=3.25 x$

Question 5

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=50$, when $x=10$

Accepted Answer

A)  $y=50 x$ 
B)  $y=\frac{500}{x}$ 
C)  $y=6 x$ 
D)  $y=5 x$ 
A)  $y=50 x$ 
B)  $y=\frac{500}{x}$ 
C)  $y=6 x$ 
D)  $y=5 x$

Question 6

Add. Simplify, if possible.
-$\frac{7}{x+y}+\frac{8}{y+x}$

Accepted Answer

A)  $\frac{-1}{x+y}$ 
B)  $\frac{15}{2 x+2 y}$ 
C)  $\frac{15}{x+y}$ 
D)  $\frac{7}{x}+\frac{8}{y}$ 
A)  $\frac{-1}{x+y}$ 
B)  $\frac{15}{2 x+2 y}$ 
C)  $\frac{15}{x+y}$ 
D)  $\frac{7}{x}+\frac{8}{y}$

Question 7

Multiply. Do not simplify.
-$\frac{x-9}{7-x} \cdot \frac{-1}{-1}$

Accepted Answer

A)  $\frac{(7-x)(-1)}{(x-9)(-1)}$ 
B)  $\frac{(x-9)(-1)}{(7-x)(-1)}$ 
C)  $\frac{x-9}{(7-x)(-1)}$ 
D)  $\frac{(x-9)(-1)}{7-x}$ 
A)  $\frac{(7-x)(-1)}{(x-9)(-1)}$ 
B)  $\frac{(x-9)(-1)}{(7-x)(-1)}$ 
C)  $\frac{x-9}{(7-x)(-1)}$ 
D)  $\frac{(x-9)(-1)}{7-x}$

Question 8

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

Accepted Answer

A)  $d=2,6$ 
B)  $d=-2$ 
C)  $d=2$ 
D)  None 
A)  $d=2,6$ 
B)  $d=-2$ 
C)  $d=2$ 
D)  None

Question 9

Solve the equation.
-$\frac{29}{\mathrm{x}}=6-\frac{1}{\mathrm{x}}$

Accepted Answer

A)  $\frac{3}{14}$ 
B)  5 
C)  4 
D)  $\frac{29}{6}$ 
A)  $\frac{3}{14}$ 
B)  5 
C)  4 
D)  $\frac{29}{6}$

Question 10

Solve the problem.
-A machine can fill 7260 cartons of milk in 0.8 hour. How many cartons of milk can it fill per hour?

Accepted Answer

A)  8067 cartons 
B)  5808 cartons 
C)  7261 cartons 
D)  9075 cartons 
A)  8067 cartons 
B)  5808 cartons 
C)  7261 cartons 
D)  9075 cartons

Question 11

Find the ratio. Simplify, if possible.
-David's paycheck for a week at the video store was $\$ 111.32$. If he worked 23 hours that week, what was his pay rate?

Accepted Answer

A)  $\$ 4.86 /$ hour 
B)  $\$ 4.61 /$ hour 
C)  $\$ 4.84 /$ hour 
D)  $\$ 5.06 /$ hour 
A)  $\$ 4.86 /$ hour 
B)  $\$ 4.61 /$ hour 
C)  $\$ 4.84 /$ hour 
D)  $\$ 5.06 /$ hour

Question 12

Find the LCM.
-$x^{2}-8 x+16, x^{2}-3 x-4$

Accepted Answer

A)  $(x-4)(x+1)$ 
B)  $(x+4)(x+4)(x+1)$ 
C)  $(x-4)(x-4)$ 
D)  $(x-4)(x-4)(x+1)$ 
A)  $(x-4)(x+1)$ 
B)  $(x+4)(x+4)(x+1)$ 
C)  $(x-4)(x-4)$ 
D)  $(x-4)(x-4)(x+1)$

Question 13

Divide and simplify.
-$\frac{z^{2}+12 z+35}{z^{2}+13 z+40} \div \frac{z^{2}+7 z}{z^{2}+18 z+80}$

Accepted Answer

A)  $z+10$ 
B)  $\frac{z}{z^{2}+13 z+40}$ 
C)  $\frac{z+10}{z^{2}+8 z}$ 
D)  $\frac{z+10}{z}$ 
A)  $z+10$ 
B)  $\frac{z}{z^{2}+13 z+40}$ 
C)  $\frac{z+10}{z^{2}+8 z}$ 
D)  $\frac{z+10}{z}$

Question 14

Find the LCM.
-$r^{2}+10 r+25, r^{2}+5 r$

Accepted Answer

A)  $r(r+1)(r+5)$ 
B)  $r(r+5)$ 
C)  $(r+5)^{2}$ 
D)  $r(r+5)^{2}$ 
A)  $r(r+1)(r+5)$ 
B)  $r(r+5)$ 
C)  $(r+5)^{2}$ 
D)  $r(r+5)^{2}$

Question 15

Solve the equation.
-$x+\frac{10}{x}=7$

Accepted Answer

A)  10 
B)  $-5,-2$ 
C)  5, 2 
D)  7,10 
A)  10 
B)  $-5,-2$ 
C)  5, 2 
D)  7,10

Question 16

Add. Simplify, if possible.
-$\frac{5}{13 x}+\frac{3}{13 x}$

Accepted Answer

A)  $\frac{8}{26 x}$ 
B)  1 
C)  $\frac{8}{13 x}$ 
D)  $\frac{13 x}{8}$ 
A)  $\frac{8}{26 x}$ 
B)  1 
C)  $\frac{8}{13 x}$ 
D)  $\frac{13 x}{8}$

Question 17

Subtract. Simplify, if possible.
-$\frac{15 x y}{x^{2}-y^{2}}-\frac{x-y}{x+y}$

Accepted Answer

A)  $\frac{-x^{2}+13 x y-y^{2}}{(x+y)(x+y)}$ 
B)  $\frac{x^{2}+13 x y+y^{2}}{(x+y)(x-y)}$ 
C)  $\frac{x^{2}+17 x y+y^{2}}{(x+y)(x-y)}$ 
D)  $\frac{-x^{2}+17 x y-y^{2}}{(x+y)(x-y)}$ 
A)  $\frac{-x^{2}+13 x y-y^{2}}{(x+y)(x+y)}$ 
B)  $\frac{x^{2}+13 x y+y^{2}}{(x+y)(x-y)}$ 
C)  $\frac{x^{2}+17 x y+y^{2}}{(x+y)(x-y)}$ 
D)  $\frac{-x^{2}+17 x y-y^{2}}{(x+y)(x-y)}$

Question 18

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

Accepted Answer

A)  $\frac{x^{2}+10 x}{x^{2}-4}$ 
B)  $\frac{-x^{2}+6 x}{x^{2}-4}$ 
C)  $\frac{x^{2}+6 x}{x^{2}-4}$ 
D)  $\frac{-x^{2}+10 x}{x^{2}-4}$ 
A)  $\frac{x^{2}+10 x}{x^{2}-4}$ 
B)  $\frac{-x^{2}+6 x}{x^{2}-4}$ 
C)  $\frac{x^{2}+6 x}{x^{2}-4}$ 
D)  $\frac{-x^{2}+10 x}{x^{2}-4}$

Question 19

Add, first finding the LCD. Simplify, if possible.
-$\frac{1}{24}+\frac{5}{54}$

Accepted Answer

A)  $\frac{29}{13}$ 
B)  $\frac{1}{216}$ 
C)  $\frac{29}{216}$ 
D)  $\frac{1}{13}$ 
A)  $\frac{29}{13}$ 
B)  $\frac{1}{216}$ 
C)  $\frac{29}{216}$ 
D)  $\frac{1}{13}$

Question 20

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=23.76$, when $x=8.8$

Accepted Answer

A)  $x=2.7 y$ 
B)  $y=0.37 x$ 
C)  $y=2.7 x$ 
D)  $y=8.8 x$ 
A)  $x=2.7 y$ 
B)  $y=0.37 x$ 
C)  $y=2.7 x$ 
D)  $y=8.8 x$

Simplify. - $\frac{\frac{x}{5 y}-\frac{2}{10 y^{3}}}{\frac{2}{10 y^{3}}-\frac{x}{5 y}}$

Solve the equation. - $\frac{1}{\mathrm{x}-4}+\frac{1}{2 \mathrm{x}-8}=\frac{3}{2}$

Multiply. Do not simplify. - $\frac{7 a+1}{5 a-1} \cdot \frac{a}{a}$

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=80$ , when $x=260$

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=50$ , when $x=10$

Add. Simplify, if possible. - $\frac{7}{x+y}+\frac{8}{y+x}$

Multiply. Do not simplify. - $\frac{x-9}{7-x} \cdot \frac{-1}{-1}$

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

Solve the equation. - $\frac{29}{\mathrm{x}}=6-\frac{1}{\mathrm{x}}$

Solve the problem. -A machine can fill 7260 cartons of milk in 0.8 hour. How many cartons of milk can it fill per hour?

Find the ratio. Simplify, if possible. -David's paycheck for a week at the video store was $\$ 111.32$ . If he worked 23 hours that week, what was his pay rate?

Find the LCM. - $x^{2}-8 x+16, x^{2}-3 x-4$

Divide and simplify. - $\frac{z^{2}+12 z+35}{z^{2}+13 z+40} \div \frac{z^{2}+7 z}{z^{2}+18 z+80}$

Find the LCM. - $r^{2}+10 r+25, r^{2}+5 r$

Solve the equation. - $x+\frac{10}{x}=7$

Add. Simplify, if possible. - $\frac{5}{13 x}+\frac{3}{13 x}$

Subtract. Simplify, if possible. - $\frac{15 x y}{x^{2}-y^{2}}-\frac{x-y}{x+y}$

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

Add, first finding the LCD. Simplify, if possible. - $\frac{1}{24}+\frac{5}{54}$

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=23.76$ , when $x=8.8$

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. - x5y−210y3210y3−x5y\frac{\frac{x}{5 y}-\frac{2}{10 y^{3}}}{\frac{2}{10 y^{3}}-\frac{x}{5 y}}10y32​−5yx​5yx​−10y32​​

Solve the equation. - 1x−4+12x−8=32\frac{1}{\mathrm{x}-4}+\frac{1}{2 \mathrm{x}-8}=\frac{3}{2}x−41​+2x−81​=23​

Multiply. Do not simplify. - 7a+15a−1⋅aa\frac{7 a+1}{5 a-1} \cdot \frac{a}{a}5a−17a+1​⋅aa​

Given the values of xxx and yyy , find an equation of variation in which yyy varies directly as xxx . - y=80y=80y=80 , when x=260x=260x=260

Given the values of xxx and yyy , find an equation of variation in which yyy varies directly as xxx . - y=50y=50y=50 , when x=10x=10x=10

Add. Simplify, if possible. - 7x+y+8y+x\frac{7}{x+y}+\frac{8}{y+x}x+y7​+y+x8​

Multiply. Do not simplify. - x−97−x⋅−1−1\frac{x-9}{7-x} \cdot \frac{-1}{-1}7−xx−9​⋅−1−1​

Find all numbers for which the rational expression is not defined. - d−62−d\frac{d-6}{2-d}2−dd−6​

Solve the equation. - 29x=6−1x\frac{29}{\mathrm{x}}=6-\frac{1}{\mathrm{x}}x29​=6−x1​