Practice Simplifying Rational Expressions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Simplifying a rational expression p(x)q(x)\frac{p(x)}{q(x)} by factoring both the numerator and denominator, then canceling common factors. The domain must exclude values that make any original denominator zero.

Just like simplifying the fraction 68=34\frac{6}{8} = \frac{3}{4} by canceling the common factor of 2, you can simplify x2โˆ’4xโˆ’2\frac{x^2 - 4}{x - 2} by factoring the top as (x+2)(xโˆ’2)(x+2)(x-2) and canceling the common (xโˆ’2)(x-2) factor. But remember: you can only cancel FACTORS (things being multiplied), not TERMS (things being added).

Showing a random 20 of 50 problems.

Example 1

hard
Simplify 2x2+7x+3x2+2xโˆ’3\frac{2x^2 + 7x + 3}{x^2 + 2x - 3}, xโ‰ โˆ’3,1x \neq -3, 1.

Example 2

medium
Simplify 2x2โˆ’8x2+4x+4\frac{2x^2 - 8}{x^2 + 4x + 4}.

Example 3

easy
Simplify 3x6x2\frac{3x}{6x^2}, xโ‰ 0x\neq0.

Example 4

medium
Simplify 3โˆ’xxโˆ’3\frac{3 - x}{x - 3}, xโ‰ 3x \neq 3.

Example 5

medium
Simplify x2โˆ’9x2+5x+6\frac{x^2 - 9}{x^2 + 5x + 6}.

Example 6

medium
Simplify x2โˆ’xโˆ’6x2โˆ’9\frac{x^2 - x - 6}{x^2 - 9} and state restrictions.

Example 7

easy
Simplify 4x22x\frac{4x^2}{2x}, xโ‰ 0x\neq0.

Example 8

easy
Simplify 2x+6x+3\frac{2x + 6}{x + 3}, xโ‰ โˆ’3x\neq-3.

Example 9

challenge
Simplify x4โˆ’16x2+4\frac{x^4 - 16}{x^2 + 4}.

Example 10

hard
Simplify x2โˆ’3xโˆ’10x2โˆ’7x+10\frac{x^2 - 3x - 10}{x^2 - 7x + 10}, xโ‰ 2,5x \neq 2, 5.

Example 11

medium
Simplify x2โˆ’25x2โˆ’10x+25\frac{x^2 - 25}{x^2 - 10x + 25}, state restrictions.

Example 12

easy
Simplify xโˆ’55โˆ’x\frac{x - 5}{5 - x}, xโ‰ 5x\neq5.

Example 13

medium
Simplify x2+7x+12x2+4x\frac{x^2 + 7x + 12}{x^2 + 4x}, xโ‰ 0,โˆ’4x \neq 0, -4.

Example 14

easy
Simplify 6x39x\frac{6x^3}{9x}, xโ‰ 0x\neq0.

Example 15

hard
Simplify x3โˆ’8x2โˆ’4\frac{x^3 - 8}{x^2 - 4}, xโ‰ ยฑ2x \neq \pm 2.

Example 16

medium
Simplify 3x2โˆ’12x2โˆ’xโˆ’2\frac{3x^2 - 12}{x^2 - x - 2}, state restrictions.

Example 17

challenge
Simplify x2โˆ’y2x2โˆ’2xy+y2\frac{x^2 - y^2}{x^2 - 2xy + y^2}, xโ‰ yx\neq y.

Example 18

medium
Simplify x3โˆ’xx2โˆ’1\frac{x^3 - x}{x^2 - 1}, xโ‰ ยฑ1x \neq \pm 1.

Example 19

medium
Simplify x3โˆ’xx2โˆ’1\frac{x^3 - x}{x^2 - 1}.

Example 20

challenge
Simplify x3โˆ’8x2โˆ’4\frac{x^3 - 8}{x^2 - 4}, state restrictions.