Factor \({x}^{2}+7x+10\).
Ask: Which two numbers add up to \(7\) and multiply to \(10\)?
Rewrite the expression using the above.
\[(x+2)(x+5)\]
\[Wr\imath tethe\times \frac{(x+2)(x+5)}{3x+6}\times \frac{6x-6}{{x}^{2}+2x-15}\]
Factor out the common term \(3\).
\[Wr\imath tethe\times \frac{(x+2)(x+5)}{3(x+2)}\times \frac{6x-6}{{x}^{2}+2x-15}\]
Factor out the common term \(6\).
\[Wr\imath tethe\times \frac{(x+2)(x+5)}{3(x+2)}\times \frac{6(x-1)}{{x}^{2}+2x-15}\]
Factor \({x}^{2}+2x-15\).
Ask: Which two numbers add up to \(2\) and multiply to \(-15\)?
Rewrite the expression using the above.
\[(x-3)(x+5)\]
\[Wr\imath tethe\times \frac{(x+2)(x+5)}{3(x+2)}\times \frac{6(x-1)}{(x-3)(x+5)}\]
Cancel \(x+5\).
\[Wr\imath tethe\times \frac{x+2}{3(x+2)}\times \frac{6(x-1)}{x-3}\]
Cancel \(x+2\).
\[Wr\imath tethe\times \frac{1}{3}\times \frac{6(x-1)}{x-3}\]
Regroup terms.
\[\frac{1}{3}tthWr\imath ee\times \frac{6(x-1)}{x-3}\]
Simplify.
\[\frac{{t}^{2}hWr\imath ee\times 6(x-1)}{3(x-3)}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{t}^{2}hWr\imath {e}^{2}\times 6(x-1)}{3(x-3)}\]
Regroup terms.
\[\frac{6Wr{e}^{2}\imath {t}^{2}h(x-1)}{3(x-3)}\]
Simplify.
\[\frac{2Wr{e}^{2}\imath {t}^{2}h(x-1)}{x-3}\]
(2*Wr*e^2*IM*t^2*h*(x-1))/(x-3)
