Free Printable Unit 2 Review (Rational Expressions and Equations)

1.

Solve: $\frac{1}{6x^2}=\frac{1}{3x^2}-\frac{1}{\ \ x\ }$

a)

$x=6$

b)

$x=\frac{1}{6}$

c)

$x=0$

d)

$Inconsistent$ (no solution)

2.

Solve: $3\left(x+5\right)=3x+16$

a)

$x=1$

b)

$x=0$

c)

$Inconsistent$ ( No solution)

d)

$Identity$ (All Real Numbers)

3.

Solve: $\frac{1}{x}=\frac{6}{5x}+1$

a)

$x=-\frac{1}{5}$

b)

$x=\frac{1}{5}$

c)

$Identity$ (All Real Numbers)

d)

$x=0$

4.

Solve: $\frac{1}{v}+\frac{3v+12}{v^{2\ }-5v}=\frac{7v-56}{v^2-5v}$

a)

$v=-21$

b)

$v=21$

c)

$v=\frac{49}{3}$

d)

$v=1$

5.

Solve: $\frac{1}{r-2}+\frac{1}{r^2-7r+10}=\frac{6}{r-2\ }$

a)

$r=\frac{34}{7}$

b)

$r=\frac{34}{5}$

c)

$Identity$

d)

$r=\frac{26}{5}$

6.

Solve and classify: $\frac{n+5}{n+8}=1+\frac{6}{n+1}$

a)

$\ n=-\frac{17}{3}$

b)

$\ n=-\frac{17}{3}$

c)

$\ n=-\frac{17}{3}$

d)

$\ n=\frac{17}{3}$

7.

Solve: $\frac{x+5}{x^2+x}=\frac{1}{x^2+x}-\frac{x-6}{x+1}$

a)

$x=4$

b)

$x=4,\ 1$

c)

$x=1$

d)

$Inconsistent$ (No Solution)

8.

Solve and classify: $1=\frac{1}{x^2+2x}+\frac{x-1}{x}$

a)

$Inconsistent$ (no solution)

b)

$\ x=-1$

c)

$\ x=1$

d)

$\ x=-1$

9.

Solve: $\frac{r+5}{r^2-2r}-1=\frac{1}{r^2-2r}$

a)

$r=4$

b)

$r=-1$

c)

$r=-4,\ 1$

d)

$r=4,\ -1$

10.

$\frac{x^2-9}{\left(x+2\right)}\div\frac{\left(x+3\right)}{\left(x+2\right)}$ Simplify this rational expression

a)

$\frac{\left(x-3\right)}{\left(x+2\right)}$

b)

$x-3$

c)

$\left(x+2\right)$

d)

$Inconsistent\ \left(No\ Solution\right)$

11.

$\frac{3}{x+1}-\frac{\left(x+2\right)}{\left(x-2\right)}$ Perform the required operation and simplify fully

a)

$\frac{-\left(x^2+8\right)}{\left(x+1\right)\left(x-2\right)}$

b)

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

c)

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

d)

$\frac{-8}{\left(x+1\right)\left(x-2\right)}$

Unit 2 Review (Rational Expressions and Equations)

Total questions: 11

Worksheet time: 55mins

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