Factor \({z}^{2}-2z-3\).
Ask: Which two numbers add up to \(-2\) and multiply to \(-3\)?
Rewrite the expression using the above.
\[(z-3)(z+1)\]
\[\frac{(z-3)(z+1)}{{z}^{2}-9}\]
Rewrite \({z}^{2}-9\) in the form \({a}^{2}-{b}^{2}\), where \(a=z\) and \(b=3\).
\[\frac{(z-3)(z+1)}{{z}^{2}-{3}^{2}}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{(z-3)(z+1)}{(z+3)(z-3)}\]
Cancel \(z-3\).
\[\frac{z+1}{z+3}\]
(z+1)/(z+3)
