Multiplying and Dividing Rational Expressions Math Example 2

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Example 2

hard
Divide x2โˆ’4x2+xรทxโˆ’2x\frac{x^2 - 4}{x^2 + x} \div \frac{x - 2}{x}.

Solution

  1. 1
    Step 1: Multiply by reciprocal: x2โˆ’4x2+xโ‹…xxโˆ’2\frac{x^2 - 4}{x^2 + x} \cdot \frac{x}{x - 2}.
  2. 2
    Step 2: Factor: (x+2)(xโˆ’2)x(x+1)โ‹…xxโˆ’2\frac{(x+2)(x-2)}{x(x+1)} \cdot \frac{x}{x-2}.
  3. 3
    Step 3: Cancel xx and (xโˆ’2)(x-2): x+2x+1\frac{x+2}{x+1}.
  4. 4
    Check: At x=3x = 3: 512รท13=54\frac{5}{12} \div \frac{1}{3} = \frac{5}{4} and 54\frac{5}{4} โœ“

Answer

x+2x+1\frac{x + 2}{x + 1}, xโ‰ 0,2x \neq 0, 2
Division of rational expressions is converted to multiplication by the reciprocal. Then factor and cancel as usual. Track all domain restrictions from both the original and the reciprocal.

About Multiplying and Dividing Rational Expressions

Multiplying rational expressions by multiplying numerators together and denominators together (after factoring and canceling). Dividing by multiplying by the reciprocal of the divisor.

Learn more about Multiplying and Dividing Rational Expressions โ†’

More Multiplying and Dividing Rational Expressions Examples

Example 1 medium

Multiply [formula].

Example 3 easy

Multiply [formula].

Example 4 medium

Divide [formula].

โ† All Multiplying and Dividing Rational Expressions Examples Multiplying and Dividing Rational Expressions Concept