Solve x/a-x=b

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

Solve for b

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

$$x\neq a$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -x+a.

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

Use the distributive property to multiply b by -x+a.

$$x=-bx+ba$$

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

$$-bx+ba=x$$

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by a-x.

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

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

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

Solve for a

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