Question

here X=??...........​

Answer 1

$\Large\sf{\underline{\underline{Question:-}}}$

$\Large\sf\dfrac{1}{x - \frac{1}{p}} + \dfrac{1}{x - \frac{1}{q}} = p + q$

$\Large\sf{\underline{\underline{Solution:-}}}$

$\Large\sf\dfrac{1}{x - \frac{1}{p}} + \dfrac{1}{x - \frac{1}{q}} = p + q$

$\Large\implies\sf\dfrac{1}{\frac{px - 1}{p}} + \dfrac{1}{\frac{qx - 1}{q}} = p + q$

$\Large\implies\sf\dfrac{p}{px - 1} + \dfrac{q}{wc - 1} = p + q$

$\Large\implies\sf\dfrac{(qx - 1) p + (px - 1) q}{(px - 1) (qx - 1)} = p + q$

$\Large\implies\sf\: pqx - p + qpx - q = (p + q) (px - 1) (qx - 1)$

$\Large\implies\sf\: 2pqx - p - q = (p²x - p + pqx - q) (qx - 1)$

$\Large\implies\sf\: 2pqx - p - q = p²x²q - p²x + p - pqx + pq²x² - pqx - q²x + q$