Solve x/b=x/c+a

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

Solve for a

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

$$c\neq 0\text{ and }b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by bc, the least common multiple of b,c.

$$cx=bx+bca$$

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

$$bx+bca=cx$$

Subtract bx from both sides.

$$bca=cx-bx$$

Divide both sides by bc.

$$\frac{bca}{bc}=\frac{x\left(c-b\right)}{bc}$$

Dividing by bc undoes the multiplication by bc.

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

Divide x\left(c-b\right) by bc.

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

Solve for b

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

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by bc, the least common multiple of b,c.

$$cx=bx+bca$$

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

$$bx+bca=cx$$

Combine all terms containing b.

$$\left(x+ca\right)b=cx$$

The equation is in standard form.

$$\left(x+ac\right)b=cx$$

Divide both sides by x+ac.

$$\frac{\left(x+ac\right)b}{x+ac}=\frac{cx}{x+ac}$$

Dividing by x+ac undoes the multiplication by x+ac.

$$b=\frac{cx}{x+ac}$$

Variable b cannot be equal to 0.

$$b=\frac{cx}{x+ac}\text{, }b\neq 0$$