Question

If $\frac{x}{pq}+\frac{x}{qr}+\frac{x}{pr}=p+q+r$, then find the value of$x$.

• A. $pqr$
• B. $\frac{pq}{r}$
• C. $\frac{p}{qr}$
• D. $\frac{q}{pr}$

Answer 1

The correct option is A $pqr$

$\frac{x}{pq}+\frac{x}{qr}+\frac{x}{pr}=p+q+r$
$\frac{rx+px+qx}{pqr}=p+q+r$
$\frac{x(p+q+r)}{pqr}=p+q+r$
Cross multiplying, we get:
$x=\frac{(p+q+r)\times pqr}{(p+q+r)}=pqr$