Solve z-a/b-z=r/x

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

Solve for a

$$a=\frac{xz+rz-br}{x}$$

$$z\neq b\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(-z+b\right), the least common multiple of b-z,x.

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

Use the distributive property to multiply x by z-a.

$$xz-xa=\left(-z+b\right)r$$

Use the distributive property to multiply -z+b by r.

$$xz-xa=-zr+br$$

Subtract xz from both sides.

$$-xa=-zr+br-xz$$

The equation is in standard form.

$$\left(-x\right)a=br-rz-xz$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{br-rz-xz}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{br-rz-xz}{-x}$$

Divide -zr+br-xz by -x.

$$a=\frac{rz-br}{x}+z$$

Solve for b

$$\left\{\begin{matrix}b=\frac{xz-ax+rz}{r}\text{, }&z\neq a\text{ and }x\neq 0\text{ and }r\neq 0\\b\neq z\text{, }&r=0\text{ and }z=a\text{ and }x\neq 0\end{matrix}\right.$$