Factor \({x}^{2}-7x+12\).
Ask: Which two numbers add up to \(-7\) and multiply to \(12\)?
Rewrite the expression using the above.
\[(x-4)(x-3)\]
\[\frac{x-4}{x+4}\times \frac{\frac{x-3}{x+3}}{\frac{(x-4)(x-3)}{{x}^{2}+7x+12}}\]
Factor \({x}^{2}+7x+12\).
Ask: Which two numbers add up to \(7\) and multiply to \(12\)?
Rewrite the expression using the above.
\[(x+3)(x+4)\]
\[\frac{x-4}{x+4}\times \frac{\frac{x-3}{x+3}}{\frac{(x-4)(x-3)}{(x+3)(x+4)}}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{(x-4)(x-3)}{(x+4)(x+3)\times \frac{(x-4)(x-3)}{(x+3)(x+4)}}\]
Cancel \(x+3\).
\[\frac{(x-4)(x-3)}{(x+4)\times \frac{(x-4)(x-3)}{x+4}}\]
Cancel \(x+4\).
\[\frac{(x-4)(x-3)}{(x-4)(x-3)}\]
Cancel \(x-3\).
\[1\]
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