Question

P=(gx)/(g+x)
solve for x

Answer 1

\[\large P=\frac{gx}{(g+x)}\]First, multiply both sides by g+x,\[\large (g+x)P=\frac{gx}{\cancel{(g+x)}}\cancel{(g+x)} \qquad \rightarrow \qquad (g+x)P=gx\]

Answer 2

Distribute the P to each term inside the brackets,\[\large Pg+Px=gx\]Subtract \(Px\) from both sides,\[\large Pg\cancel{+Px-Px}=gx-Px \qquad \rightarrow \qquad Pg=gx-Px\]

Answer 3

Factor an \(\large x\) out of each term on the right,\[\large Pg=x(g-P)\]

Then finally, divide both sides by \((g-P)\).\[\large \frac{Pg}{(g-P)}=\frac{x\cancel{(g-P)}}{\cancel{(g-P)}} \qquad \qquad \rightarrow \qquad \qquad \frac{Pg}{(g-P)}=x\]