How do you evaluate \frac { x ^ { 2} - 9} { x + 7} \div \frac { ( x + 3) } { 1}?

Sep 13, 2017

$= 1 - \frac{10}{x + 7}$

Explanation:

firstly, change using the rules of fractions change to a multiplication problem

$\frac{{x}^{2} - 9}{x + 7} \div \frac{x + 3}{1}$

$\implies \frac{{x}^{2} - 9}{x + 7} \times \frac{1}{x + 3}$

secondly, factorise and cancel where possible

$\frac{\cancel{\left(x + 3\right)} \left(x - 3\right)}{x + 7} \times \frac{1}{\cancel{\left(x + 3\right)}}$

$= \frac{x - 3}{x + 7}$

lastly change from an improper fraction

$= \frac{\left(x + 7\right) - 10}{x + 7}$

$= \frac{x + 7}{x + 7} - \frac{10}{x + 7}$

$= 1 - \frac{10}{x + 7}$