Free Printable Solving Rational Equations

1.

For what value(s) of $m$ is the expression $\frac{m^2-2m+1}{2m^2+m-3}$ undefined?

a)

$-\frac{3}{2},\ 0,\ 1$

b)

$-1,\ \frac{3}{2}$

c)

$-\frac{3}{2},\ 1$

d)

$\frac{3}{2}$

2.

Simplify the following expression: $\frac{x^2+5x+4}{x^2+2x+1}\times\frac{2x+2}{x+4}$

a)

$\frac{1}{2}$

b)

$2$

c)

$\frac{\left(x+4\right)^2}{2\left(x+1\right)^2}$

d)

$\frac{x+4}{2\left(x+1\right)}$

3.

Simplify the following expression:
$\frac{a+b}{3}\div\frac{a^2+b^2}{12}$

a)

$\frac{a+b}{4\left(a^2+b^2\right)}$

b)

$\frac{4}{a+b}$

c)

$\frac{a+b}{4}$

d)

$\frac{4\left(a+b\right)}{a^2+b^2}$

4.

What is the equation(s) of the vertical asymptote(s) of the graph of $f\left(x\right)=\frac{x^2+5x+6}{x-1}$ ?

a)

$x=1$

b)

$x=-2$

c)

$x=-2,\ x=-3$

d)

$f\left(x\right)=1$

5.

Which rational function is graphed?

a)

$\frac{3}{x+2}$

b)

$\frac{3}{x-2}$

c)

$\frac{x}{x+2}$

d)

$\frac{x}{x-2}$

6.

The distance a car can travel on a certain amount of fuel varies INVERSELY with its speed. If a car traveling 50 miles per hour can travel 300 miles on 10 gallons of fuel, how far could the car travel on 10 gallons of fuel at 60 miles per hour?

a)

250 miles

b)

360 miles

c)

275 miles

d)

300 miles

7.

Solve $\frac{n}{n-4}+n=\frac{12-4n}{n-4}$

a)

$n=-4,\ n=3$

b)

$n=-3,\ n=4$

c)

$n=-4$

d)

$n=3$

8.

Tomas can do a job in 4 hours. Julia can do the same job in 6 hours. How many hours will it take the two of them to do the job if they work together?

a)

3.5 hours

b)

2.4 hours

c)

5 hours

d)

2 hours

9.

Solve the following equation for x:
$\frac{12}{x}+\frac{3}{4}=\frac{3}{2}$

a)

16

b)

4

c)

5

d)

8

10.

Solve for s:
$\frac{s}{s+2}+s=\frac{5s+8}{s+2}$

a)

2

b)

4

c)

6

d)

8

11.

Solve for w:
$\frac{4}{w-2}=\frac{-1}{w+3}$

a)

2

b)

-2

c)

4

d)

-4

12.

Solve for x:
$\frac{6}{x-1}=\frac{4}{x-2}+\frac{2}{x+1}$

a)

1

b)

2

c)

-1

d)

No Solution

13.

Simplify the following expression:
$\frac{9y^2-1}{2y-1}\times\frac{1-2y}{3y-1}$

a)

$-3y-1$

b)

$3y+1$

c)

$-3y+1$

d)

$3y-1$

14.

What is the function of the graph?

a)

$f\left(x\right)=\frac{4}{x+2}+2$

b)

$f\left(x\right)=\frac{4}{x-2}-2$

c)

$f\left(x\right)=\frac{4}{x+2}-2$

d)

$f\left(x\right)=\frac{4}{x-2}+2$

15.

The ratio of two less than a number to six more than that number is 2:3. Which of the following numbers is it?

a)

8

b)

18

c)

22

d)

24

Solving Rational Equations

Total questions: 15

Worksheet time: 45mins

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