Solve BC/PR=CA/PQ

$$\frac { BC } { PR } = \frac { CA } { PQ }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{BQ}{R}\text{, }&P\neq 0\text{ and }R\neq 0\text{ and }Q\neq 0\\A\in \mathrm{C}\text{, }&C=0\text{ and }R\neq 0\text{ and }P\neq 0\text{ and }Q\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by PQR, the least common multiple of PR,PQ.

$$QBC=RCA$$

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

$$RCA=QBC$$

The equation is in standard form.

$$CRA=BCQ$$

Divide both sides by RC.

$$\frac{CRA}{CR}=\frac{BCQ}{CR}$$

Dividing by RC undoes the multiplication by RC.

$$A=\frac{BCQ}{CR}$$

Divide QBC by RC.

$$A=\frac{BQ}{R}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=\frac{AR}{Q}\text{, }&P\neq 0\text{ and }R\neq 0\text{ and }Q\neq 0\\B\in \mathrm{C}\text{, }&C=0\text{ and }R\neq 0\text{ and }P\neq 0\text{ and }Q\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by PQR, the least common multiple of PR,PQ.

$$QBC=RCA$$

Reorder the terms.

$$BCQ=ACR$$

The equation is in standard form.

$$CQB=ACR$$

Divide both sides by CQ.

$$\frac{CQB}{CQ}=\frac{ACR}{CQ}$$

Dividing by CQ undoes the multiplication by CQ.

$$B=\frac{ACR}{CQ}$$

Divide ACR by CQ.

$$B=\frac{AR}{Q}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{BQ}{R}\text{, }&P\neq 0\text{ and }R\neq 0\text{ and }Q\neq 0\\A\in \mathrm{R}\text{, }&C=0\text{ and }R\neq 0\text{ and }P\neq 0\text{ and }Q\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by PQR, the least common multiple of PR,PQ.

$$QBC=RCA$$

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

$$RCA=QBC$$

The equation is in standard form.

$$CRA=BCQ$$

Divide both sides by RC.

$$\frac{CRA}{CR}=\frac{BCQ}{CR}$$

Dividing by RC undoes the multiplication by RC.

$$A=\frac{BCQ}{CR}$$

Divide QBC by RC.

$$A=\frac{BQ}{R}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{AR}{Q}\text{, }&P\neq 0\text{ and }R\neq 0\text{ and }Q\neq 0\\B\in \mathrm{R}\text{, }&C=0\text{ and }R\neq 0\text{ and }P\neq 0\text{ and }Q\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by PQR, the least common multiple of PR,PQ.

$$QBC=RCA$$

Reorder the terms.

$$BCQ=ACR$$

The equation is in standard form.

$$CQB=ACR$$

Divide both sides by CQ.

$$\frac{CQB}{CQ}=\frac{ACR}{CQ}$$

Dividing by CQ undoes the multiplication by CQ.

$$B=\frac{ACR}{CQ}$$

Divide ACR by CQ.

$$B=\frac{AR}{Q}$$