Verified Answer :

\(\frac{7}{8}p-\frac{1}{4}=\frac{1}{2}p \\\\ \frac{7p}{8}-\frac{1}{4}^{(2}=\frac{p}{2}^{(4} \\\\ 7p-2=4p\\\\7p-4p=2 \\\\3p=2\\\\ \boxed{p=\frac{2}{3}}\)

if you mean \(\frac{7}{8p} - \frac{1}{4}=\frac{1}{2p}\)
then multiply by p to give \(\frac{7}{8}-\frac{p}{4}=\frac{1}{2}\)
then multiply by 8 to give \(7-2p=4\)
subtract 7 \(-2p=-3\)
divide by -2 \(p=\frac{3}{2}\)

if you mean \((\frac{7}{8})p-\frac{1}{4}=(\frac{1}{2})\)
then multiply by 8 to give \(7p-2=4p\)
subtract 4p \(3p-2=0\)
add 2 \(3p=2\)
then divide by 3 \(p=\frac{2}{3}\)

hope that helps