Chapter 6, Problem 17AR

To determine

To simplify the fraction $\frac{b^2-25}{b^2-12b+35}$ .

Answer to Problem 17AR

  $\frac{b^2-25}{b^2-12b+35}=\frac{b+5}{b-7}$

Explanation of Solution

Given:

  $\frac{b^2-25}{b^2-12b+35}$

Calculation:

  $\begin{array}{l}\frac{b^2-25}{b^2-12b+35}=\frac{b^2-5^2}{b^2-5b-7b+35}\\ =\frac{\left(b-5\right)\left(b+5\right)}{b\left(b-5\right)-7\left(b-5\right)}\\ =\frac{\left(b-5\right)\left(b+5\right)}{\left(b-5\right)\left(b-7\right)}\\ =\frac{b+5}{b-7}\end{array}$