Question

$frac{p {}^{2} - 11p + 10 }{20 + 8p - p {}^{2} }$
​

Answer 1

$displaystyle tt frac{p^2-11p+10}{20+8p-p^2}=frac{p^2-p-10p+10}{-p^2+8p+20}=frac{p(p-1)-10(p-1)}{-p^2+10p-2p+20}=frac{(p-1)(p-10)}{-p(p-10)-2(p-10)}=frac{(p-1)(p-10)}{-(p-10)(p+2)}=frac{(p-1) cdot (-1)}{p+2}=-frac{p-1}{p+2}=boxed{bold{frac{1-p}{p+2}}}$