Question 1

Find the LCM.
-$4 a-12, a^{2}-3 a$

Accepted Answer

A)  $4 a^{2}-3$ 
B)  $4 \mathrm{a}(\mathrm{a}-3)$ 
C)  $4 a^{2}-12$ 
D)  $4 \mathrm{a}-3$ 
A)  $4 a^{2}-3$ 
B)  $4 \mathrm{a}(\mathrm{a}-3)$ 
C)  $4 a^{2}-12$ 
D)  $4 \mathrm{a}-3$

Question 2

Solve the problem.
-Dr. Wong can see 12 patients in 3 hours. At this rate, how long would it take her to see 24 patients?

Accepted Answer

A)  36 hours 
B)  6 hours 
C)  96 hours 
D)  5 hours 
A)  36 hours 
B)  6 hours 
C)  96 hours 
D)  5 hours

Question 3

Simplify.
-$\frac{8-2 x}{x-4}$

Accepted Answer

A)  $x-4$ 
B)  $2 x-8$ 
C)  -2 
D)  2 
A)  $x-4$ 
B)  $2 x-8$ 
C)  -2 
D)  2

Question 4

Find the reciprocal.
-$\frac{x}{7}$

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true.
-$y=5.25$, when $x=0.24$

Accepted Answer

A)  $y=21.88 x$ 
B)  $y=\frac{1.66}{x}$ 
C)  $y=\frac{1.26}{x}$ 
D)  $y=\frac{21.88}{x}$ 
A)  $y=21.88 x$ 
B)  $y=\frac{1.66}{x}$ 
C)  $y=\frac{1.26}{x}$ 
D)  $y=\frac{21.88}{x}$

Question 7

Solve the problem.
-The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 10 miles per hour in 15 minutes, how fast must it travel to cover the same distance in 30 minutes?

Accepted Answer

A)  45 miles per hour 
B)  $\frac{1}{20}$ miles per hour 
C)  20 miles per hour 
D)  5 miles per hour 
A)  45 miles per hour 
B)  $\frac{1}{20}$ miles per hour 
C)  20 miles per hour 
D)  5 miles per hour

Question 8

Find the LCM.
-$60,24,90$

Accepted Answer

A)  360 
B)  120 
C)  72 
D)  180 
A)  360 
B)  120 
C)  72 
D)  180

Question 9

Find the reciprocal.
-$\frac{x^{2}+8}{2-x}$

Accepted Answer

A)  $\frac{8-x}{x^{2}+2}$ 
B)  $\frac{x^{2}+8}{x-2}$ 
C)  $\frac{x^{2}+2}{8-x}$ 
D)  $\frac{2-x}{x^{2}+8}$ 
A)  $\frac{8-x}{x^{2}+2}$ 
B)  $\frac{x^{2}+8}{x-2}$ 
C)  $\frac{x^{2}+2}{8-x}$ 
D)  $\frac{2-x}{x^{2}+8}$

Question 10

Add. Simplify, if possible.
-$\frac{4}{y^{2}-3 y+2}+\frac{6}{y^{2}-1}$

Accepted Answer

A)  $\frac{48 y-8}{(y-1)(y+1)(y-2)}$ 
B)  $\frac{8 y-10}{(y-1)(y+1)(y-2)}$ 
C)  $\frac{10 y-8}{(y-1)(y+1)(y-2)}$ 
D)  $\frac{10 y-8}{(y-1)(y-2)}$ 
A)  $\frac{48 y-8}{(y-1)(y+1)(y-2)}$ 
B)  $\frac{8 y-10}{(y-1)(y+1)(y-2)}$ 
C)  $\frac{10 y-8}{(y-1)(y+1)(y-2)}$ 
D)  $\frac{10 y-8}{(y-1)(y-2)}$

Question 11

Solve the problem.
-Fred bicycles $5 \mathrm{~km} / \mathrm{h}$ slower than Samantha. In the time it takes Fred to bicycle $56 \mathrm{~km}$, Samantha travels $76 \mathrm{~km}$. How fast does Fred bicycle?

Accepted Answer

A)  $9 \mathrm{~km} / \mathrm{h}$ 
B)  $19 \mathrm{~km} / \mathrm{h}$ 
C)  $28 \mathrm{~km} / \mathrm{h}$ 
D)  $14 \mathrm{~km} / \mathrm{h}$ 
A)  $9 \mathrm{~km} / \mathrm{h}$ 
B)  $19 \mathrm{~km} / \mathrm{h}$ 
C)  $28 \mathrm{~km} / \mathrm{h}$ 
D)  $14 \mathrm{~km} / \mathrm{h}$

Question 12

Simplify.
-$\frac{\frac{1}{5}-\frac{1}{y}}{\frac{5-y}{5}}$

Accepted Answer

A)  $\frac{-1}{y}$ 
B)  $\frac{1}{y}$ 
C)  $\frac{-5}{y}$ 
D)  $-\mathrm{y}$ 
A)  $\frac{-1}{y}$ 
B)  $\frac{1}{y}$ 
C)  $\frac{-5}{y}$ 
D)  $-\mathrm{y}$

Question 13

Solve the problem.
-A loaded moving truck is traveling $20 \mathrm{mph}$ faster than a freight train. In the time it takes the train to travel 120 miles, the truck travels 200 miles. Find the speed of the truck.

Accepted Answer

A)  $20 \mathrm{mph}$ 
B)  $100 \mathrm{mph}$ 
C)  $50 \mathrm{mph}$ 
D)  $10 \mathrm{mph}$ 
A)  $20 \mathrm{mph}$ 
B)  $100 \mathrm{mph}$ 
C)  $50 \mathrm{mph}$ 
D)  $10 \mathrm{mph}$

Question 14

Add, first finding the LCD. Simplify, if possible.
-$\frac{8}{9}+\frac{2}{7}$

Accepted Answer

A)  $\frac{37}{8}$ 
B)  $\frac{10}{63}$ 
C)  $\frac{74}{63}$ 
D)  $\frac{5}{8}$ 
A)  $\frac{37}{8}$ 
B)  $\frac{10}{63}$ 
C)  $\frac{74}{63}$ 
D)  $\frac{5}{8}$

Question 15

Add. Simplify, if possible.
-$\frac{6}{8}+\frac{4}{8}$

Accepted Answer

A)  5 
B)  $\frac{5}{4}$ 
C)  $\frac{4}{5}$ 
D)  $\frac{5}{2}$ 
A)  5 
B)  $\frac{5}{4}$ 
C)  $\frac{4}{5}$ 
D)  $\frac{5}{2}$

Question 16

Divide and simplify.
-$\frac{x^{2}-64}{x} \div \frac{3 x+24}{x-8}$

Accepted Answer

A)  $\frac{3(x+8)^{2}}{x}$ 
B)  $\frac{3 x}{(x-8)^{2}}$ 
C)  $\frac{(x-8)^{2}}{x}$ 
D)  $\frac{(x-8)^{2}}{3 x}$ 
A)  $\frac{3(x+8)^{2}}{x}$ 
B)  $\frac{3 x}{(x-8)^{2}}$ 
C)  $\frac{(x-8)^{2}}{x}$ 
D)  $\frac{(x-8)^{2}}{3 x}$

Question 17

Add. Simplify, if possible.
-$\frac{9}{x^{4} y}+\frac{7}{x y^{3}}$

Accepted Answer

A)  $\frac{16}{x y}$ 
B)  $\frac{7 x^{4}+9 y^{3}}{x^{4} y^{3}}$ 
C)  $\frac{7 x^{3}+9 y^{2}}{x^{4} y^{3}}$ 
D)  $\frac{16}{x^{4} y^{3}}$ 
A)  $\frac{16}{x y}$ 
B)  $\frac{7 x^{4}+9 y^{3}}{x^{4} y^{3}}$ 
C)  $\frac{7 x^{3}+9 y^{2}}{x^{4} y^{3}}$ 
D)  $\frac{16}{x^{4} y^{3}}$

Question 18

Find the reciprocal.
-$\frac{x^{2}+2 x y-y^{2}}{x^{2}-6 x y+y^{2}}$

Accepted Answer

A)  $\frac{x^{2}+6 x y+y^{2}}{x^{2}-2 x y-y^{2}}$ 
B)  $\frac{x^{2}-2 x y+y^{2}}{x^{2}+6 x y-y^{2}}$ 
C)  $\frac{1}{x^{2}-6 x y-y^{2}}$ 
D)  $\frac{x^{2}-6 x y+y^{2}}{x^{2}+2 x y-y^{2}}$ 
A)  $\frac{x^{2}+6 x y+y^{2}}{x^{2}-2 x y-y^{2}}$ 
B)  $\frac{x^{2}-2 x y+y^{2}}{x^{2}+6 x y-y^{2}}$ 
C)  $\frac{1}{x^{2}-6 x y-y^{2}}$ 
D)  $\frac{x^{2}-6 x y+y^{2}}{x^{2}+2 x y-y^{2}}$

Question 19

Solve the equation.
-$\frac{4}{x+6}=\frac{6}{x-5}$

Accepted Answer

A)  $-\frac{11}{2}$ 
B)  -28 
C)  $\frac{28}{5}$ 
D)  - 8 
A)  $-\frac{11}{2}$ 
B)  -28 
C)  $\frac{28}{5}$ 
D)  - 8

Question 20

Find all numbers for which the rational expression is not defined.
-$\frac{2}{a-7}$

Accepted Answer

A)  $\mathrm{a}=0$ 
B)  $\mathrm{a}=7$ 
C)  None 
D)  $\mathrm{a}=-7$ 
A)  $\mathrm{a}=0$ 
B)  $\mathrm{a}=7$ 
C)  None 
D)  $\mathrm{a}=-7$

Find the LCM. - $4 a-12, a^{2}-3 a$

Solve the problem. -Dr. Wong can see 12 patients in 3 hours. At this rate, how long would it take her to see 24 patients?

Simplify. - $\frac{8-2 x}{x-4}$

Find the reciprocal. - $\frac{x}{7}$

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

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=5.25$ , when $x=0.24$

Solve the problem. -The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 10 miles per hour in 15 minutes, how fast must it travel to cover the same distance in 30 minutes?

Find the LCM. - $60,24,90$

Find the reciprocal. - $\frac{x^{2}+8}{2-x}$

Add. Simplify, if possible. - $\frac{4}{y^{2}-3 y+2}+\frac{6}{y^{2}-1}$

Solve the problem. -Fred bicycles $5 \mathrm{~km} / \mathrm{h}$ slower than Samantha. In the time it takes Fred to bicycle $56 \mathrm{~km}$ , Samantha travels $76 \mathrm{~km}$ . How fast does Fred bicycle?

Simplify. - $\frac{\frac{1}{5}-\frac{1}{y}}{\frac{5-y}{5}}$

Solve the problem. -A loaded moving truck is traveling $20 \mathrm{mph}$ faster than a freight train. In the time it takes the train to travel 120 miles, the truck travels 200 miles. Find the speed of the truck.

Add, first finding the LCD. Simplify, if possible. - $\frac{8}{9}+\frac{2}{7}$

Add. Simplify, if possible. - $\frac{6}{8}+\frac{4}{8}$

Divide and simplify. - $\frac{x^{2}-64}{x} \div \frac{3 x+24}{x-8}$

Add. Simplify, if possible. - $\frac{9}{x^{4} y}+\frac{7}{x y^{3}}$

Find the reciprocal. - $\frac{x^{2}+2 x y-y^{2}}{x^{2}-6 x y+y^{2}}$

Solve the equation. - $\frac{4}{x+6}=\frac{6}{x-5}$

Find all numbers for which the rational expression is not defined. - $\frac{2}{a-7}$

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

Find the LCM. - 4a−12,a2−3a4 a-12, a^{2}-3 a4a−12,a2−3a

Solve the problem. -Dr. Wong can see 12 patients in 3 hours. At this rate, how long would it take her to see 24 patients?

Simplify. - 8−2xx−4\frac{8-2 x}{x-4}x−48−2x​

Find the reciprocal. - x7\frac{x}{7}7x​

Subtract. Simplify, if possible. - 7z2−3z−3z−3\frac{7}{z^{2}-3 z}-\frac{3}{z-3}z2−3z7​−z−33​

Find an equation of variation in which yyy varies inversely as xxx and the following is true. - y=5.25y=5.25y=5.25 , when x=0.24x=0.24x=0.24