Question

Make p the subjet in 2/r+1/p=1/q​

Answer 1

well, let's notice the denominators, hmmm so we can use as the LCD say the expression of "rpq", so, let's multiply both sides by the LCD of "rpq" to do away with the denominators.

$\cfrac{2}{r}+\cfrac{1}{p}=\cfrac{1}{q}\implies \stackrel{\textit{multiplying both sides by } ~~ \stackrel{LCD}{rpq}}{rpq\left( \cfrac{2}{r}+\cfrac{1}{p} \right)=rpq\left( \cfrac{1}{q} \right)}\implies 2pq+1rq=1rp \\\\\\ 2pq+rq=rp\implies rq=rp-2pq\implies rq=\stackrel{\textit{common factoring}}{p(r-2q)}\implies \cfrac{rq}{r-2q}=p$