Solve A=(A+xS)/Q

$$A = ( A + x S ) / Q$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{Sx}{Q-1}\text{, }&Q\neq 1\text{ and }Q\neq 0\\A\in \mathrm{C}\text{, }&\left(x=0\text{ or }S=0\right)\text{ and }Q=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{A+xS}{Q} from both sides.

$$A-\frac{A+xS}{Q}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply A times \frac{Q}{Q}.

$$\frac{AQ}{Q}-\frac{A+xS}{Q}=0$$

Since \frac{AQ}{Q} and \frac{A+xS}{Q} have the same denominator, subtract them by subtracting their numerators.

$$\frac{AQ-\left(A+xS\right)}{Q}=0$$

Do the multiplications in AQ-\left(A+xS\right).

$$\frac{AQ-A-xS}{Q}=0$$

Multiply both sides of the equation by Q.

$$AQ-A-xS=0$$

Add xS to both sides. Anything plus zero gives itself.

$$AQ-A=xS$$

Combine all terms containing A.

$$\left(Q-1\right)A=xS$$

The equation is in standard form.

$$\left(Q-1\right)A=Sx$$

Divide both sides by Q-1.

$$\frac{\left(Q-1\right)A}{Q-1}=\frac{Sx}{Q-1}$$

Dividing by Q-1 undoes the multiplication by Q-1.

$$A=\frac{Sx}{Q-1}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{Sx}{Q-1}\text{, }&Q\neq 1\text{ and }Q\neq 0\\A\in \mathrm{R}\text{, }&\left(x=0\text{ or }S=0\right)\text{ and }Q=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{A+xS}{Q} from both sides.

$$A-\frac{A+xS}{Q}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply A times \frac{Q}{Q}.

$$\frac{AQ}{Q}-\frac{A+xS}{Q}=0$$

Since \frac{AQ}{Q} and \frac{A+xS}{Q} have the same denominator, subtract them by subtracting their numerators.

$$\frac{AQ-\left(A+xS\right)}{Q}=0$$

Do the multiplications in AQ-\left(A+xS\right).

$$\frac{AQ-A-xS}{Q}=0$$

Multiply both sides of the equation by Q.

$$AQ-A-xS=0$$

Add xS to both sides. Anything plus zero gives itself.

$$AQ-A=xS$$

Combine all terms containing A.

$$\left(Q-1\right)A=xS$$

The equation is in standard form.

$$\left(Q-1\right)A=Sx$$

Divide both sides by Q-1.

$$\frac{\left(Q-1\right)A}{Q-1}=\frac{Sx}{Q-1}$$

Dividing by Q-1 undoes the multiplication by Q-1.

$$A=\frac{Sx}{Q-1}$$

Solve for Q

$$\left\{\begin{matrix}Q=\frac{Sx+A}{A}\text{, }&A\neq -Sx\text{ and }A\neq 0\\Q\neq 0\text{, }&\left(x=0\text{ or }S=0\right)\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable Q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Q.

$$AQ=A+xS$$

The equation is in standard form.

$$AQ=Sx+A$$

Divide both sides by A.

$$\frac{AQ}{A}=\frac{Sx+A}{A}$$

Dividing by A undoes the multiplication by A.

$$Q=\frac{Sx+A}{A}$$

Variable Q cannot be equal to 0.

$$Q=\frac{Sx+A}{A}\text{, }Q\neq 0$$