Multiplying and Dividing Rational Expressions Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Divide x+5xโˆ’1รทx+5x2โˆ’1\frac{x + 5}{x - 1} \div \frac{x + 5}{x^2 - 1}.

Solution

  1. 1
    Flip: x+5xโˆ’1โ‹…x2โˆ’1x+5=x+5xโˆ’1โ‹…(x+1)(xโˆ’1)x+5\frac{x+5}{x-1} \cdot \frac{x^2 - 1}{x+5} = \frac{x+5}{x-1} \cdot \frac{(x+1)(x-1)}{x+5}.
  2. 2
    Cancel: x+1x + 1.

Answer

x+1x + 1, xโ‰ 1,โˆ’1,โˆ’5x \neq 1, -1, -5
After flipping the divisor, the (x+5)(x+5) and (xโˆ’1)(x-1) factors cancel. The restrictions come from all original denominators and the divisor's numerator.

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 2 hard

Divide [formula].

Example 3 easy

Multiply [formula].

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