Answer
$= \frac{(7p+5)}{(3p-8)}$
Work Step by Step
$\frac{28p^{2}+41p+15}{6p^{2}+11p-72} \div \frac{4p^{2}+7p+3}{2p^{2}+11p+9}$
$= \frac{28p^{2}+41p+15}{6p^{2}+11p-72} \times \frac{2p^{2}+11p+9}{4p^{2}+7p+3}$
$= \frac{28p^{2}+20p+21p+15}{6p^{2}+27p-16p-72} \times \frac{2p^{2}+9p+2p+9}{4p^{2}+4p+3p+3}$
$= \frac{4p(7p+5)+3(7p+5)}{3p(2p+9)-8(2p+9)} \times \frac{p(2p+9)+1(2p+9)}{4p(p+1)+3(p+1)}$
$= \frac{(4p+3)(7p+5)}{(3p-8)(2p+9)} \times \frac{(p+1)(2p+9)}{(4p+3)(p+1)}$
$= \frac{(4p+3)(7p+5)}{(3p-8)} \times \frac{(p+1)}{(4p+3)(p+1)}$
$= \frac{(7p+5)}{(3p-8)} \times \frac{(p+1)}{(p+1)}$
$= \frac{(7p+5)}{(3p-8)} \times \frac{1}{1}$
$= \frac{(7p+5)}{(3p-8)} \times 1$
$= \frac{(7p+5)}{(3p-8)}$
