Solve h=x-a/x+b

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

Solve for a

$$a=-hx+x-bh$$

$$x\neq -b$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+b.

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

Use the distributive property to multiply h by x+b.

$$hx+hb=x-a$$

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

$$x-a=hx+hb$$

Subtract x from both sides.

$$-a=hx+hb-x$$

The equation is in standard form.

$$-a=hx-x+bh$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{hx-x+bh}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{hx-x+bh}{-1}$$

Divide -x+hx+hb by -1.

$$a=-hx+x-bh$$

Solve for b

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