Solve x=x/a+b

$$x = \frac { x } { a } + b$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{x}{b-x}\text{, }&x\neq 0\text{ and }x\neq b\\a\neq 0\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xa=x+ab$$

Subtract ab from both sides.

$$xa-ab=x$$

Combine all terms containing a.

$$\left(x-b\right)a=x$$

Divide both sides by x-b.

$$\frac{\left(x-b\right)a}{x-b}=\frac{x}{x-b}$$

Dividing by x-b undoes the multiplication by x-b.

$$a=\frac{x}{x-b}$$

Variable a cannot be equal to 0.

$$a=\frac{x}{x-b}\text{, }a\neq 0$$

Solve for b

$$b=\frac{x\left(a-1\right)}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$xa=x+ab$$

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

$$x+ab=xa$$

Subtract x from both sides.

$$ab=xa-x$$

The equation is in standard form.

$$ab=ax-x$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{x\left(a-1\right)}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{x\left(a-1\right)}{a}$$