🎥 Watch Video Solution
Q. \( \frac{(p+\frac{1}{q})^{p-q}(p-\frac{1}{q})^{p+q}}{(q+\frac{1}{p})^{p-q}(q-\frac{1}{p})^{p+q}} = \left(\frac{p}{q}\right)^x \)
✏️ Solution
\( = \frac{\left(\frac{pq+1}{q}\right)^{p-q}\left(\frac{pq-1}{q}\right)^{p+q}}{\left(\frac{pq+1}{p}\right)^{p-q}\left(\frac{pq-1}{p}\right)^{p+q}} \)
\( = \frac{(pq+1)^{p-q}(pq-1)^{p+q}}{q^{p-q}q^{p+q}} \div \frac{(pq+1)^{p-q}(pq-1)^{p+q}}{p^{p-q}p^{p+q}} \)
\( = \frac{1}{q^{2p}} \div \frac{1}{p^{2p}} \)
\( = \frac{p^{2p}}{q^{2p}} \)
\( = \left(\frac{p}{q}\right)^{2p} \)
\( x = 2p \)
\( \boxed{2p} \)