Solve x-a/x-b=c

$$x - a / x - b = c$$

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xx-a-bx=cx$$

Multiply x and x to get x^{2}.

$$x^{2}-a-bx=cx$$

Subtract x^{2} from both sides.

$$-a-bx=cx-x^{2}$$

Add bx to both sides.

$$-a=cx-x^{2}+bx$$

The equation is in standard form.

$$-a=cx+bx-x^{2}$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x\left(c-x+b\right) by -1.

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

Solve for b

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xx-a-bx=cx$$

Multiply x and x to get x^{2}.

$$x^{2}-a-bx=cx$$

Subtract x^{2} from both sides.

$$-a-bx=cx-x^{2}$$

Add a to both sides.

$$-bx=cx-x^{2}+a$$

The equation is in standard form.

$$\left(-x\right)b=a+cx-x^{2}$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=\frac{a+cx-x^{2}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=\frac{a+cx-x^{2}}{-x}$$

Divide cx-x^{2}+a by -x.

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