Answer
$x=\frac{pqs}{q+p}$
Work Step by Step
$\frac{x}{p}+\frac{x}{q}=s$
Find the least common multiplier of p, q: pq
Multiply by LCM=pq
$\frac{x}{p}pq+\frac{x}{q}pq=spq$
simplify
$xq+xp=pqs=$
Factor xq+xp
$xq+xp$
factor out common term
$=x\left(q+p\right)$
$x\left(q+p\right)=pqs$
Divide both sides by q+p
$\frac{x\left(q+p\right)}{q+p}=\frac{pqs}{q+p}$
Simplify
$x=\frac{pqs}{q+p}$
