Question 1

Given the values of $x$ and $y$, find an equation of variation in which $y$ varies directly as $x$.
-$y=28$, when $x=8$

Accepted Answer

A)  $y=3.5 y$ 
B)  $y=3.5 x$ 
C)  $y=28 x$ 
D)  $y=0.29 x$ 
A)  $y=3.5 y$ 
B)  $y=3.5 x$ 
C)  $y=28 x$ 
D)  $y=0.29 x$

Question 2

Find all numbers for which the rational expression is not defined.
-$\frac{c-9}{5}$

Accepted Answer

A)  $c=0$ 
B)  $c=-9$ 
C)  None 
D)  $\mathrm{c}=9$ 
A)  $c=0$ 
B)  $c=-9$ 
C)  None 
D)  $\mathrm{c}=9$

Question 3

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

Accepted Answer

A)  $\frac{-14}{y-3}$ 
B)  $\frac{5}{y-3}$ 
C)  $\frac{9}{y-3}$ 
D)  $\frac{-9}{y-3}$ 
A)  $\frac{-14}{y-3}$ 
B)  $\frac{5}{y-3}$ 
C)  $\frac{9}{y-3}$ 
D)  $\frac{-9}{y-3}$

Question 4

Write the word or phrase that best completes each statement or answers the question
-For $x \neq 3$, the rational expression $\frac{8(x-3)}{x-3}$ is equal to 8 . Can the same be said for $\frac{8 x-3}{x-3}$ ? Explain why or why not.

Accepted Answer

A) True 
 B)False

Question 5

Simplify.
-$\frac{y^{2}-2 y-8}{y^{2}+3 y-28}$

Accepted Answer

A)  $\frac{-2 y-8}{3 y-28}$ 
B)  $\frac{-2 y-2}{3 y-7}$ 
C)  $\frac{y+2}{y+7}$ 
D)  $-\frac{y^{2}-2 y-8}{y^{2}+3 y-28}$ 
A)  $\frac{-2 y-8}{3 y-28}$ 
B)  $\frac{-2 y-2}{3 y-7}$ 
C)  $\frac{y+2}{y+7}$ 
D)  $-\frac{y^{2}-2 y-8}{y^{2}+3 y-28}$

Question 6

Solve the equation.
-$\frac{3}{y}=\frac{y}{2 y-3}$

Accepted Answer

A)  $-3,3$ 
B)  $-3,-3$ 
C)  $3,-3$ 
D)  3,3 
A)  $-3,3$ 
B)  $-3,-3$ 
C)  $3,-3$ 
D)  3,3

Question 7

Subtract. Simplify, if possible.
-$\frac{3}{14 x}-\frac{9}{10 x^{2}}$

Accepted Answer

A)  $-\frac{6}{140 x^{2}}$ 
B)  $\frac{-6}{14 x+10 x^{2}}$ 
C)  $\frac{18}{70 x^{2}}$ 
D)  $\frac{3(5 x-21)}{70 x^{2}}$ 
A)  $-\frac{6}{140 x^{2}}$ 
B)  $\frac{-6}{14 x+10 x^{2}}$ 
C)  $\frac{18}{70 x^{2}}$ 
D)  $\frac{3(5 x-21)}{70 x^{2}}$

Question 8

Find the reciprocal.
-$4 y^{2}+5 y$

Accepted Answer

A)  $1-\left(4 y^{2}+5 y\right)$ 
B)  $\frac{1}{4 y^{2}+5 y}$ 
C)  $5 y^{2}+4 y$ 
D)  $\frac{4 y^{2}}{5 y}$ 
A)  $1-\left(4 y^{2}+5 y\right)$ 
B)  $\frac{1}{4 y^{2}+5 y}$ 
C)  $5 y^{2}+4 y$ 
D)  $\frac{4 y^{2}}{5 y}$

Question 9

Find the reciprocal.
-$\frac{10}{y}$

Accepted Answer

A)  $-\frac{10}{\mathrm{y}}$ 
B)  $1-\frac{10}{\mathrm{y}}$ 
C)  $\frac{y}{10}$ 
D)  $\frac{1}{10 \mathrm{y}}$ 
A)  $-\frac{10}{\mathrm{y}}$ 
B)  $1-\frac{10}{\mathrm{y}}$ 
C)  $\frac{y}{10}$ 
D)  $\frac{1}{10 \mathrm{y}}$

Question 10

Solve the equation.
-$\frac{9}{x+1}=\frac{5}{x}$

Accepted Answer

A)  $\frac{5}{14}$ 
B)  $-\frac{5}{4}$ 
C)  $\frac{5}{4}$ 
D)  $\frac{4}{5}$ 
A)  $\frac{5}{14}$ 
B)  $-\frac{5}{4}$ 
C)  $\frac{5}{4}$ 
D)  $\frac{4}{5}$

Question 11

Subtract. Simplify, if possible.
-$\frac{9 x}{x^{2}-5 x+6}-\frac{36}{x^{2}-6 x+8}$

Accepted Answer

A)  $\frac{9}{(x-2)(x-3)}$ 
B)  $\frac{9(x-6)}{(x-3)(x-4)}$ 
C)  $\frac{9 x-36}{(x-2)(x-3)(x-4)}$ 
D)  $\frac{x-6}{(x-3)(x-4)}$ 
A)  $\frac{9}{(x-2)(x-3)}$ 
B)  $\frac{9(x-6)}{(x-3)(x-4)}$ 
C)  $\frac{9 x-36}{(x-2)(x-3)(x-4)}$ 
D)  $\frac{x-6}{(x-3)(x-4)}$

Question 12

Add. Simplify, if possible.
-$\frac{4}{m-n^{2}}+\frac{9}{n^{2}-m}$

Accepted Answer

A)  $\frac{5}{m-n^{2}}$ 
B)  $\frac{13}{m-n^{2}}$ 
C)  $\frac{36}{m-n^{2}}$ 
D)  $\frac{-5}{m-n^{2}}$ 
A)  $\frac{5}{m-n^{2}}$ 
B)  $\frac{13}{m-n^{2}}$ 
C)  $\frac{36}{m-n^{2}}$ 
D)  $\frac{-5}{m-n^{2}}$

Question 13

Divide and simplify.
-$\frac{5}{9} \div \frac{9}{4}$

Accepted Answer

A)  $\frac{5}{4}$ 
B)  $\frac{4}{5}$ 
C)  $\frac{20}{81}$ 
D)  $\frac{81}{20}$ 
A)  $\frac{5}{4}$ 
B)  $\frac{4}{5}$ 
C)  $\frac{20}{81}$ 
D)  $\frac{81}{20}$

Question 14

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

Accepted Answer

A)  $\frac{12 y+27}{14 y+45}$ 
B)  $\frac{y^{2}+3 y}{y+5}$ 
C)  $\frac{y+3}{y+5}$ 
D)  $\frac{y+3}{y^{2}+5 y}$ 
A)  $\frac{12 y+27}{14 y+45}$ 
B)  $\frac{y^{2}+3 y}{y+5}$ 
C)  $\frac{y+3}{y+5}$ 
D)  $\frac{y+3}{y^{2}+5 y}$

Question 15

Write the word or phrase that best completes each statement or answers the question
-Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

Accepted Answer

To multiply rational expressions, you fi

Question 16

Solve the problem.
-The mass of a liquid varies directly as its volume $\mathrm{V}$. If the mass of the liquid in a cubical container $5 \mathrm{~cm}$ on a side is $250 \mathrm{~g}$, find the mass of the liquid in a cubical container $3 \mathrm{~cm}$ on a side.

Accepted Answer

A)  $6 \mathrm{~g}$ 
B)  $27 \mathrm{~g}$ 
C)  $54 \mathrm{~g}$ 
D)  $12 \mathrm{~g}$ 
A)  $6 \mathrm{~g}$ 
B)  $27 \mathrm{~g}$ 
C)  $54 \mathrm{~g}$ 
D)  $12 \mathrm{~g}$

Question 17

Multiply. Do not simplify.
-$\frac{3 x}{3 x} \cdot \frac{x-3}{x+10}$

Accepted Answer

A)  $\frac{3 x(x-3)}{x+10}$ 
B)  $\frac{3 x(x+10)}{3 x(x-3)}$ 
C)  $\frac{x-3}{3 x(x+10)}$ 
D)  $\frac{3 x(x-3)}{3 x(x+10)}$ 
A)  $\frac{3 x(x-3)}{x+10}$ 
B)  $\frac{3 x(x+10)}{3 x(x-3)}$ 
C)  $\frac{x-3}{3 x(x+10)}$ 
D)  $\frac{3 x(x-3)}{3 x(x+10)}$

Question 18

Add. Simplify, if possible.
-$\frac{x+5}{x-8}+\frac{x-4}{8-x}+\frac{9(x+1)}{x-8}$

Accepted Answer

A)  $\frac{9 x+18}{(x-8)^{3}}$ 
B)  $\frac{9 x+18}{x-8}$ 
C)  $\frac{11 x+10}{x-8}$ 
D)  $\frac{9 x+10}{x-8}$ 
A)  $\frac{9 x+18}{(x-8)^{3}}$ 
B)  $\frac{9 x+18}{x-8}$ 
C)  $\frac{11 x+10}{x-8}$ 
D)  $\frac{9 x+10}{x-8}$

Question 19

Solve the problem.
-If the area of a rectangle is fixed, the length of the rectangle varies inversely as the width. If the length of a rectangle is 25 inches and its width is 45 inches, find the length of a rectangle with a width of 15 inches.

Accepted Answer

A)  $\frac{3}{25}$ inches 
B)  75 inches 
C)  $\frac{25}{3}$ inches 
D)  27 inches 
A)  $\frac{3}{25}$ inches 
B)  75 inches 
C)  $\frac{25}{3}$ inches 
D)  27 inches

Question 20

Multiply and, if possible, simplify.
-$\frac{5 p-5}{p} \cdot \frac{5 p^{2}}{6 p-6}$

Accepted Answer

A)  $\frac{6}{25 p}$ 
B)  $\frac{25 p^{3}-25 p^{2}}{6 p^{2}-6 p}$ 
C)  $\frac{25 p}{6}$ 
D)  $\frac{30 p^{2}+60 p+30}{5 p^{3}}$ 
A)  $\frac{6}{25 p}$ 
B)  $\frac{25 p^{3}-25 p^{2}}{6 p^{2}-6 p}$ 
C)  $\frac{25 p}{6}$ 
D)  $\frac{30 p^{2}+60 p+30}{5 p^{3}}$

Given the values of $x$ and $y$ , find an equation of variation in which $y$ varies directly as $x$ . - $y=28$ , when $x=8$

Find all numbers for which the rational expression is not defined. - $\frac{c-9}{5}$

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

Write the word or phrase that best completes each statement or answers the question -For $x \neq 3$ , the rational expression $\frac{8(x-3)}{x-3}$ is equal to 8 . Can the same be said for $\frac{8 x-3}{x-3}$ ? Explain why or why not.

Simplify. - $\frac{y^{2}-2 y-8}{y^{2}+3 y-28}$

Solve the equation. - $\frac{3}{y}=\frac{y}{2 y-3}$

Subtract. Simplify, if possible. - $\frac{3}{14 x}-\frac{9}{10 x^{2}}$

Find the reciprocal. - $4 y^{2}+5 y$

Find the reciprocal. - $\frac{10}{y}$

Solve the equation. - $\frac{9}{x+1}=\frac{5}{x}$

Subtract. Simplify, if possible. - $\frac{9 x}{x^{2}-5 x+6}-\frac{36}{x^{2}-6 x+8}$

Add. Simplify, if possible. - $\frac{4}{m-n^{2}}+\frac{9}{n^{2}-m}$

Divide and simplify. - $\frac{5}{9} \div \frac{9}{4}$

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

Write the word or phrase that best completes each statement or answers the question -Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

Solve the problem. -The mass of a liquid varies directly as its volume $\mathrm{V}$ . If the mass of the liquid in a cubical container $5 \mathrm{~cm}$ on a side is $250 \mathrm{~g}$ , find the mass of the liquid in a cubical container $3 \mathrm{~cm}$ on a side.

Multiply. Do not simplify. - $\frac{3 x}{3 x} \cdot \frac{x-3}{x+10}$

Add. Simplify, if possible. - $\frac{x+5}{x-8}+\frac{x-4}{8-x}+\frac{9(x+1)}{x-8}$

Solve the problem. -If the area of a rectangle is fixed, the length of the rectangle varies inversely as the width. If the length of a rectangle is 25 inches and its width is 45 inches, find the length of a rectangle with a width of 15 inches.

Multiply and, if possible, simplify. - $\frac{5 p-5}{p} \cdot \frac{5 p^{2}}{6 p-6}$

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

Given the values of xxx and yyy , find an equation of variation in which yyy varies directly as xxx . - y=28y=28y=28 , when x=8x=8x=8

Find all numbers for which the rational expression is not defined. - c−95\frac{c-9}{5}5c−9​

Subtract. Simplify, if possible. - −2y−3−73−y\frac{-2}{y-3}-\frac{7}{3-y}y−3−2​−3−y7​

Write the word or phrase that best completes each statement or answers the question -For x≠3x \neq 3x=3 , the rational expression 8(x−3)x−3\frac{8(x-3)}{x-3}x−38(x−3)​ is equal to 8 . Can the same be said for 8x−3x−3\frac{8 x-3}{x-3}x−38x−3​ ? Explain why or why not.

Simplify. - y2−2y−8y2+3y−28\frac{y^{2}-2 y-8}{y^{2}+3 y-28}y2+3y−28y2−2y−8​

Solve the equation. - 3y=y2y−3\frac{3}{y}=\frac{y}{2 y-3}y3​=2y−3y​

Subtract. Simplify, if possible. - 314x−910x2\frac{3}{14 x}-\frac{9}{10 x^{2}}14x3​−10x29​

Find the reciprocal. - 4y2+5y4 y^{2}+5 y4y2+5y

Find the reciprocal. - 10y\frac{10}{y}y10​

Solve the equation. - 9x+1=5x\frac{9}{x+1}=\frac{5}{x}x+19​=x5​

Subtract. Simplify, if possible. - 9xx2−5x+6−36x2−6x+8\frac{9 x}{x^{2}-5 x+6}-\frac{36}{x^{2}-6 x+8}x2−5x+69x​−x2−6x+836​

Add. Simplify, if possible. - 4m−n2+9n2−m\frac{4}{m-n^{2}}+\frac{9}{n^{2}-m}m−n24​+n2−m9​

Divide and simplify. - 59÷94\frac{5}{9} \div \frac{9}{4}95​÷49​

Simplify. - y2+3yy2+5y\frac{y^{2}+3 y}{y^{2}+5 y}y2+5yy2+3y​