Question

What would be the simplest form? With steps please

Answer 1

`\displaystyle\\ (p^2-9p)/(p^2-4p - 45) - (2)/(p+5)=\\\\ =\frac{p(p-9)}{p^2 \underbrace{+5p-9p}_(=-4p) - 45} - (2)/(p+5)=\\\\\\ =(p(p-9))/(p(p+5)-9(p +5)) - (2)/(p+5)=\\\\ =(p(p-9))/((p+5)(p-9)) - (2)/(p+5)=\\\\ =(p)/(p+5) - (2)/(p+5)=\boxed{\bold{(p-2)/(p+5)}}`

Answer 2

`\bf \cfrac{p^2-9p}{p^2-4p-45}-\cfrac{2}{p+5}\qquad \begin{array}{lcclll} p^2&-4p&-45\\ &\uparrow &\uparrow \\ &5-9&5\cdot -9 \end{array}\qquad thus \\\\\\ \cfrac{p\underline{(p-9)}}{\underline{(p-9)}(p+5)}-\cfrac{2}{p+5}\implies \cfrac{p}{p+5}-\cfrac{2}{p+5}\impliedby \textit{LCD of p+5} \\\\\\ \cfrac{p-2}{p+5}`