Solve ST=1/2PQ-1/3PQ

$$ST = \frac { 1 } { 2 } PQ - \frac { 1 } { 3 } PQ$$

Solve for P

$$\left\{\begin{matrix}P=\frac{6ST}{Q}\text{, }&Q\neq 0\\P\in \mathrm{R}\text{, }&\left(S=0\text{ or }T=0\right)\text{ and }Q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine \frac{1}{2}PQ and -\frac{1}{3}PQ to get \frac{1}{6}PQ.

$$ST=\frac{1}{6}PQ$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{6}PQ=ST$$

The equation is in standard form.

$$\frac{Q}{6}P=ST$$

Divide both sides by \frac{1}{6}Q.

$$\frac{6\times \frac{Q}{6}P}{Q}=\frac{6ST}{Q}$$

Dividing by \frac{1}{6}Q undoes the multiplication by \frac{1}{6}Q.

$$P=\frac{6ST}{Q}$$

Solve for Q

$$\left\{\begin{matrix}Q=\frac{6ST}{P}\text{, }&P\neq 0\\Q\in \mathrm{R}\text{, }&\left(S=0\text{ or }T=0\right)\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine \frac{1}{2}PQ and -\frac{1}{3}PQ to get \frac{1}{6}PQ.

$$ST=\frac{1}{6}PQ$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{6}PQ=ST$$

The equation is in standard form.

$$\frac{P}{6}Q=ST$$

Divide both sides by \frac{1}{6}P.

$$\frac{6\times \frac{P}{6}Q}{P}=\frac{6ST}{P}$$

Dividing by \frac{1}{6}P undoes the multiplication by \frac{1}{6}P.

$$Q=\frac{6ST}{P}$$