Solve (1)x/a-x/b=c

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

Solve for a

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

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 ab, the least common multiple of a,b.

$$1bx-ax=cab$$

Subtract cab from both sides.

$$1bx-ax-cab=0$$

Reorder the terms.

$$bx-ax-abc=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$-ax-abc=-bx$$

Combine all terms containing a.

$$\left(-x-bc\right)a=-bx$$

Divide both sides by -x-bc.

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

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

$$a=-\frac{bx}{-x-bc}$$

Divide -bx by -x-bc.

$$a=\frac{bx}{x+bc}$$

Variable a cannot be equal to 0.

$$a=\frac{bx}{x+bc}\text{, }a\neq 0$$

Solve for b

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

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 ab, the least common multiple of a,b.

$$1bx-ax=cab$$

Subtract cab from both sides.

$$1bx-ax-cab=0$$

Reorder the terms.

$$bx-ax-abc=0$$

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

$$bx-abc=ax$$

Combine all terms containing b.

$$\left(x-ac\right)b=ax$$

Divide both sides by x-ac.

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

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

$$b=\frac{ax}{x-ac}$$

Variable b cannot be equal to 0.

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