Chapter 11.2, Problem 40PPE

To determine

Divide: $\frac{x^2+10x-11}{x^2+12x+11}÷(x-1)$

Answer to Problem 40PPE

  $\frac{x^2+10x-11}{x^2+12x+11}÷(x-1)=\frac{1}{x+1}$

Explanation of Solution

Given:

Divide: $\frac{x^2+10x-11}{x^2+12x+11}÷(x-1)$

Concept Used:

For division of rational expression, we always flip the 2^nd expression and put a multiplication sign.

Rule: $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}·\frac{d}{c}$

Calculation:

  $\begin{array}{l}\frac{x^2+10x-11}{x^2+12x+11}÷(x-1)\\ \frac{x^2+10x-11}{x^2+12x+11}·\frac{1}{x-1}\\ \frac{(x+11)(x-1)}{(x+11)(x+1)}·\frac{1}{x-1}=\frac{(x+11)}{(x+11)}·\frac{(x-1)}{(x-1)}·\frac{1}{x+1}=\frac{1}{x+1}\end{array}$

Thus, $\frac{x^2+10x-11}{x^2+12x+11}÷(x-1)=\frac{1}{x+1}$