Question 1

Simplify.
-$\frac{16 x-4}{20}$

Accepted Answer

A)  $\frac{4 x-1}{5}$ 
B)  $\frac{4 x}{5}$ 
C)  $\frac{4 x-1}{20}$ 
D)  $4 x-1$ 
A)  $\frac{4 x-1}{5}$ 
B)  $\frac{4 x}{5}$ 
C)  $\frac{4 x-1}{20}$ 
D)  $4 x-1$

Question 2

Solve the problem.
-A contractor finds that it takes Sam Tockett 9 hours to construct a wall of a certain size. It takes Jim Lowell 7 hours to construct the same wall. How long would it take if they worked together?

Accepted Answer

A)  16 hours 
B)  $\frac{16}{63}$ of an hour 
C)  1 hour 
D)  $3 \frac{15}{16}$ hours 
A)  16 hours 
B)  $\frac{16}{63}$ of an hour 
C)  1 hour 
D)  $3 \frac{15}{16}$ hours

Question 3

Multiply and, if possible, simplify.
-$\frac{3 x^{2}}{5} \cdot \frac{10}{x^{3}}$

Accepted Answer

A)  $\frac{x}{16}$ 
B)  $\frac{6 x^{2}}{x^{3}}$ 
C)  $\frac{x^{5}}{16}$ 
D)  $\frac{6}{x}$ 
A)  $\frac{x}{16}$ 
B)  $\frac{6 x^{2}}{x^{3}}$ 
C)  $\frac{x^{5}}{16}$ 
D)  $\frac{6}{x}$

Question 4

Add. Simplify, if possible.
-$\frac{5}{2-m}+\frac{4}{m-2}$

Accepted Answer

A)  $\frac{1}{2-m}$ 
B)  $\frac{20}{2-m}$ 
C)  $\frac{-1}{2-m}$ 
D)  $\frac{9}{2-m}$ 
A)  $\frac{1}{2-m}$ 
B)  $\frac{20}{2-m}$ 
C)  $\frac{-1}{2-m}$ 
D)  $\frac{9}{2-m}$

Question 5

Perform the indicated operation. Simplify, if possible.
-$\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

Accepted Answer

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

Question 6

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

Accepted Answer

A)  $\frac{15 x^{2}-7 x y+4 y^{2}}{3 x^{2} y^{2}}$ 
B)  $\frac{-15 x^{2}+23 x y+4 y^{2}}{3 x^{2} y^{2}}$ 
C)  $\frac{8 x^{2} y^{2}+4 x y^{3}-15 x^{3} y+15 x^{2} y^{2}}{3 x^{3} y^{3}}$ 
D)  $\frac{3 x+9 y}{3 x^{2} y^{2}}$ 
A)  $\frac{15 x^{2}-7 x y+4 y^{2}}{3 x^{2} y^{2}}$ 
B)  $\frac{-15 x^{2}+23 x y+4 y^{2}}{3 x^{2} y^{2}}$ 
C)  $\frac{8 x^{2} y^{2}+4 x y^{3}-15 x^{3} y+15 x^{2} y^{2}}{3 x^{3} y^{3}}$ 
D)  $\frac{3 x+9 y}{3 x^{2} y^{2}}$

Question 7

Find the LCM.
-$m^{2}+4 m, m^{2}+7 m+12$

Accepted Answer

A)  $m(m+1)^{2}$ 
B)  $m(m+4)(m+3)$ 
C)  $m(x+1)(m+3)$ 
D)  $(m+1)^{2}$ 
A)  $m(m+1)^{2}$ 
B)  $m(m+4)(m+3)$ 
C)  $m(x+1)(m+3)$ 
D)  $(m+1)^{2}$

Question 8

If the rational expression $\frac{8 x^{9} y^{5}}{7 p^{6} q}$ represents the area of a rectangle and $\frac{7 x^{8} y^{3}}{p^{5}}$ represents the length of the rectangle, what rational expression represents the width?

Accepted Answer

A)  $\frac{8 x^{17} y^{8}}{p^{11} q}$ 
B)  $\frac{8 x y^{2}}{49 p q}$ 
C)  $\frac{8 x^{17} y^{8}}{49 p^{11} q}$ 
D)  $\frac{8 x y^{2}}{14 \mathrm{pq}}$ 
A)  $\frac{8 x^{17} y^{8}}{p^{11} q}$ 
B)  $\frac{8 x y^{2}}{49 p q}$ 
C)  $\frac{8 x^{17} y^{8}}{49 p^{11} q}$ 
D)  $\frac{8 x y^{2}}{14 \mathrm{pq}}$

Question 9

Subtract. Simplify, if possible.
-$\frac{24}{q-7}-\frac{7}{q-7}$

Accepted Answer

A)  $\frac{24(q-7)}{7(q-7)}$ 
B)  $\frac{31}{q-7}$ 
C)  $\frac{17}{q-7}$ 
D)  $\frac{17}{q}$ 
A)  $\frac{24(q-7)}{7(q-7)}$ 
B)  $\frac{31}{q-7}$ 
C)  $\frac{17}{q-7}$ 
D)  $\frac{17}{q}$

Question 10

Find the LCM.
-$10,6,15$

Accepted Answer

A)  15 
B)  10 
C)  6 
D)  30 
A)  15 
B)  10 
C)  6 
D)  30

Question 11

Simplify.
-$\frac{x+4+\frac{4}{x}}{x+5+\frac{6}{x}}$

Accepted Answer

A)  $\frac{x+2}{x+3}$ 
B)  $\frac{x+2}{x^{2}+3 x}$ 
C)  $\frac{x^{2}+4 x+4}{x^{2}+5 x+6}$ 
D)  $\frac{(x+2)^{2}}{x+3}$ 
A)  $\frac{x+2}{x+3}$ 
B)  $\frac{x+2}{x^{2}+3 x}$ 
C)  $\frac{x^{2}+4 x+4}{x^{2}+5 x+6}$ 
D)  $\frac{(x+2)^{2}}{x+3}$

Question 12

Add. Simplify, if possible.
-$\frac{6}{9 x-7}+\frac{1}{7-9 x}$

Accepted Answer

A)  $\frac{7}{9 x-7}$ 
B)  $\frac{-5}{9 x-7}$ 
C)  $\frac{5}{9 x-7}$ 
D)  $\frac{-7}{9 x-7}$ 
A)  $\frac{7}{9 x-7}$ 
B)  $\frac{-5}{9 x-7}$ 
C)  $\frac{5}{9 x-7}$ 
D)  $\frac{-7}{9 x-7}$

Question 13

Find the ratio. Simplify, if possible.
-Mara can type 1485 words in $\frac{3}{4}$ hour (45 minutes). How many words per minute can she type?

Accepted Answer

A)  44 words/minute 
B)  25 words/minute 
C)  33 words/minute 
D)  1114 words/minute 
A)  44 words/minute 
B)  25 words/minute 
C)  33 words/minute 
D)  1114 words/minute

Question 14

Find the reciprocal.
-$\frac{y^{2}+12 y+3}{y^{2}-y+11}$

Accepted Answer

A)  $\frac{y^{2}-3 y+12}{y^{2}+y+11}$ 
B)  $\frac{y^{2}+12 y-3}{y^{2}-y-11}$ 
C)  $\frac{y^{2}-y+11}{y^{2}+12 y+3}$ 
D)  $\frac{y^{2}-y-11}{y^{2}+12 y-3}$ 
A)  $\frac{y^{2}-3 y+12}{y^{2}+y+11}$ 
B)  $\frac{y^{2}+12 y-3}{y^{2}-y-11}$ 
C)  $\frac{y^{2}-y+11}{y^{2}+12 y+3}$ 
D)  $\frac{y^{2}-y-11}{y^{2}+12 y-3}$

Question 15

For the pair of similar triangles, find the length of the indicated side.
-  In the left triangle, the hypotenuse has length 10 , and the longer leg has length 8 . In the right triangle, the hypotenuse has length 5 , the longer leg has length 4 , and the shorter leg has length 3 . Find the length, $x$, of the shorter leg of the left triangle.

Accepted Answer

A)  $x=9$ 
B)  $x=3$ 
C)  $x=4$ 
D)  $x=6$ 
A)  $x=9$ 
B)  $x=3$ 
C)  $x=4$ 
D)  $x=6$

Question 16

Divide and simplify.
-$\frac{a^{2}+3 a-28}{a^{2}-14 a+49} \div \frac{a^{2}-8 a+16}{a^{2}+6 a-7}$

Accepted Answer

A)  $-\frac{a-1}{a-4}$ 
B)  $\frac{(a+7)^{2}(a-1)}{(a-7)^{2}(a-4)}$ 
C)  $\frac{(a+7)^{2}(a-1)}{(a-7)^{2}}$ 
D)  $\frac{(a-4)^{3}}{(a-7)^{2}(a-1)}$ 
A)  $-\frac{a-1}{a-4}$ 
B)  $\frac{(a+7)^{2}(a-1)}{(a-7)^{2}(a-4)}$ 
C)  $\frac{(a+7)^{2}(a-1)}{(a-7)^{2}}$ 
D)  $\frac{(a-4)^{3}}{(a-7)^{2}(a-1)}$

Question 17

Subtract. Simplify, if possible.
-$\frac{2 x+6}{x^{2}+7 x+10}-\frac{x+1}{x^{2}+7 x+10}$

Accepted Answer

A)  $\frac{7}{x^{2}+7 x+10}$ 
B)  $x+5$ 
C)  $\frac{x+7}{x^{2}+7 x+10}$ 
D)  $\frac{1}{x+2}$ 
A)  $\frac{7}{x^{2}+7 x+10}$ 
B)  $x+5$ 
C)  $\frac{x+7}{x^{2}+7 x+10}$ 
D)  $\frac{1}{x+2}$

Question 18

Perform the indicated operation. Simplify, if possible.
-$\frac{25 x}{3(5 x+1)}-\frac{1}{3 x(5 x+1)}+\frac{12}{x}$

Accepted Answer

A)  $\frac{25 x^{2}+180 x+35}{3 x}$ 
B)  $\frac{25 x^{2}+180 x+35}{15 x^{2}+3 x}$ 
C)  $\frac{5(x+7)}{15 x^{2}+3 x}$ 
D)  $\frac{5(x+7)}{3 x}$ 
A)  $\frac{25 x^{2}+180 x+35}{3 x}$ 
B)  $\frac{25 x^{2}+180 x+35}{15 x^{2}+3 x}$ 
C)  $\frac{5(x+7)}{15 x^{2}+3 x}$ 
D)  $\frac{5(x+7)}{3 x}$

Question 19

Find the ratio. Simplify, if possible.
-If Alison's company charged $\$ 88.64$ for 4 hours of work, how much did they charge per hour?

Accepted Answer

A)  $\$ 22.16 /$ hour 
B)  $\$ 4.00 /$ hour 
C)  $\$ 29.55 /$ hour 
D)  $\$ 26.16 /$ hour 
A)  $\$ 22.16 /$ hour 
B)  $\$ 4.00 /$ hour 
C)  $\$ 29.55 /$ hour 
D)  $\$ 26.16 /$ hour

Question 20

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true.
-$y=23$, when $x=3$

Accepted Answer

A)  $y=\frac{26}{x}$ 
B)  $y=\frac{7.67}{x}$ 
C)  $y=\frac{69}{x}$ 
D)  $y=7.67 x$ 
A)  $y=\frac{26}{x}$ 
B)  $y=\frac{7.67}{x}$ 
C)  $y=\frac{69}{x}$ 
D)  $y=7.67 x$

Simplify. - $\frac{16 x-4}{20}$

Solve the problem. -A contractor finds that it takes Sam Tockett 9 hours to construct a wall of a certain size. It takes Jim Lowell 7 hours to construct the same wall. How long would it take if they worked together?

Multiply and, if possible, simplify. - $\frac{3 x^{2}}{5} \cdot \frac{10}{x^{3}}$

Add. Simplify, if possible. - $\frac{5}{2-m}+\frac{4}{m-2}$

Perform the indicated operation. Simplify, if possible. - $\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

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

Find the LCM. - $m^{2}+4 m, m^{2}+7 m+12$

If the rational expression $\frac{8 x^{9} y^{5}}{7 p^{6} q}$ represents the area of a rectangle and $\frac{7 x^{8} y^{3}}{p^{5}}$ represents the length of the rectangle, what rational expression represents the width?

Subtract. Simplify, if possible. - $\frac{24}{q-7}-\frac{7}{q-7}$

Find the LCM. - $10,6,15$

Simplify. - $\frac{x+4+\frac{4}{x}}{x+5+\frac{6}{x}}$

Add. Simplify, if possible. - $\frac{6}{9 x-7}+\frac{1}{7-9 x}$

Find the ratio. Simplify, if possible. -Mara can type 1485 words in $\frac{3}{4}$ hour (45 minutes). How many words per minute can she type?

Find the reciprocal. - $\frac{y^{2}+12 y+3}{y^{2}-y+11}$

Divide and simplify. - $\frac{a^{2}+3 a-28}{a^{2}-14 a+49} \div \frac{a^{2}-8 a+16}{a^{2}+6 a-7}$

Subtract. Simplify, if possible. - $\frac{2 x+6}{x^{2}+7 x+10}-\frac{x+1}{x^{2}+7 x+10}$

Perform the indicated operation. Simplify, if possible. - $\frac{25 x}{3(5 x+1)}-\frac{1}{3 x(5 x+1)}+\frac{12}{x}$

Find the ratio. Simplify, if possible. -If Alison's company charged $\$ 88.64$ for 4 hours of work, how much did they charge per hour?

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=23$ , when $x=3$

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. - 16x−420\frac{16 x-4}{20}2016x−4​

Solve the problem. -A contractor finds that it takes Sam Tockett 9 hours to construct a wall of a certain size. It takes Jim Lowell 7 hours to construct the same wall. How long would it take if they worked together?

Multiply and, if possible, simplify. - 3x25⋅10x3\frac{3 x^{2}}{5} \cdot \frac{10}{x^{3}}53x2​⋅x310​

Add. Simplify, if possible. - 52−m+4m−2\frac{5}{2-m}+\frac{4}{m-2}2−m5​+m−24​

Perform the indicated operation. Simplify, if possible. - 2aba2−b2−ba−b+4\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4a2−b22ab​−a−bb​+4

Subtract. Simplify, if possible. - 8x+4y3x2y−5x−5yxy2\frac{8 x+4 y}{3 x^{2} y}-\frac{5 x-5 y}{x y^{2}}3x2y8x+4y​−xy25x−5y​

Find the LCM. - m2+4m,m2+7m+12m^{2}+4 m, m^{2}+7 m+12m2+4m,m2+7m+12

If the rational expression 8x9y57p6q\frac{8 x^{9} y^{5}}{7 p^{6} q}7p6q8x9y5​ represents the area of a rectangle and 7x8y3p5\frac{7 x^{8} y^{3}}{p^{5}}p57x8y3​ represents the length of the rectangle, what rational expression represents the width?

Subtract. Simplify, if possible. - 24q−7−7q−7\frac{24}{q-7}-\frac{7}{q-7}q−724​−q−77​

Find the LCM. - 10,6,1510,6,1510,6,15

Simplify. - x+4+4xx+5+6x\frac{x+4+\frac{4}{x}}{x+5+\frac{6}{x}}x+5+x6​x+4+x4​​

Add. Simplify, if possible. - 69x−7+17−9x\frac{6}{9 x-7}+\frac{1}{7-9 x}9x−76​+7−9x1​

Find the ratio. Simplify, if possible. -Mara can type 1485 words in 34\frac{3}{4}43​ hour (45 minutes). How many words per minute can she type?

Find the reciprocal. - y2+12y+3y2−y+11\frac{y^{2}+12 y+3}{y^{2}-y+11}y2−y+11y2+12y+3​

Divide and simplify. - a2+3a−28a2−14a+49÷a2−8a+16a2+6a−7\frac{a^{2}+3 a-28}{a^{2}-14 a+49} \div \frac{a^{2}-8 a+16}{a^{2}+6 a-7}a2−14a+49a2+3a−28​÷a2+6a−7a2−8a+16​

Subtract. Simplify, if possible. - 2x+6x2+7x+10−x+1x2+7x+10\frac{2 x+6}{x^{2}+7 x+10}-\frac{x+1}{x^{2}+7 x+10}x2+7x+102x+6​−x2+7x+10x+1​

Perform the indicated operation. Simplify, if possible. - 25x3(5x+1)−13x(5x+1)+12x\frac{25 x}{3(5 x+1)}-\frac{1}{3 x(5 x+1)}+\frac{12}{x}3(5x+1)25x​−3x(5x+1)1​+x12​

Find the ratio. Simplify, if possible. -If Alison's company charged $88.64\$ 88.64$88.64 for 4 hours of work, how much did they charge per hour?

Find an equation of variation in which yyy varies inversely as xxx and the following is true. - y=23y=23y=23 , when x=3x=3x=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

Simplify. - $\frac{16 x-4}{20}$

Multiply and, if possible, simplify. - $\frac{3 x^{2}}{5} \cdot \frac{10}{x^{3}}$

Add. Simplify, if possible. - $\frac{5}{2-m}+\frac{4}{m-2}$

Perform the indicated operation. Simplify, if possible. - $\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

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

Find the LCM. - $m^{2}+4 m, m^{2}+7 m+12$

If the rational expression $\frac{8 x^{9} y^{5}}{7 p^{6} q}$ represents the area of a rectangle and $\frac{7 x^{8} y^{3}}{p^{5}}$ represents the length of the rectangle, what rational expression represents the width?

Subtract. Simplify, if possible. - $\frac{24}{q-7}-\frac{7}{q-7}$

Find the LCM. - $10,6,15$

Simplify. - $\frac{x+4+\frac{4}{x}}{x+5+\frac{6}{x}}$

Add. Simplify, if possible. - $\frac{6}{9 x-7}+\frac{1}{7-9 x}$

Find the ratio. Simplify, if possible. -Mara can type 1485 words in $\frac{3}{4}$ hour (45 minutes). How many words per minute can she type?

Find the reciprocal. - $\frac{y^{2}+12 y+3}{y^{2}-y+11}$

Divide and simplify. - $\frac{a^{2}+3 a-28}{a^{2}-14 a+49} \div \frac{a^{2}-8 a+16}{a^{2}+6 a-7}$

Subtract. Simplify, if possible. - $\frac{2 x+6}{x^{2}+7 x+10}-\frac{x+1}{x^{2}+7 x+10}$

Perform the indicated operation. Simplify, if possible. - $\frac{25 x}{3(5 x+1)}-\frac{1}{3 x(5 x+1)}+\frac{12}{x}$

Find the ratio. Simplify, if possible. -If Alison's company charged $\$ 88.64$ for 4 hours of work, how much did they charge per hour?

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=23$ , when $x=3$