Solve z-a/a-1-3=a+2-2/-2-1

$$\frac { z - a } { a - 1 - 3 } = \frac { a + 2 - 2 } { - 2 - 1 }$$

Solve for z

$$z=-\frac{a\left(a-7\right)}{3}$$

$$a\neq 4$$

Solution Steps

Multiply both sides of the equation by a-4.

$$z-a=\left(-\frac{1}{3}a+\frac{4}{3}\right)\left(a+2-2\right)$$

Subtract 2 from 2 to get 0.

$$z-a=\left(-\frac{1}{3}a+\frac{4}{3}\right)a$$

Use the distributive property to multiply -\frac{1}{3}a+\frac{4}{3} by a.

$$z-a=-\frac{1}{3}a^{2}+\frac{4}{3}a$$

Add a to both sides.

$$z=-\frac{1}{3}a^{2}+\frac{4}{3}a+a$$

Combine \frac{4}{3}a and a to get \frac{7}{3}a.

$$z=-\frac{1}{3}a^{2}+\frac{7}{3}a$$

Solve for a

$$\left\{\begin{matrix}a=\frac{-\sqrt{49-12z}+7}{2}\text{, }&z\leq \frac{49}{12}\\a=\frac{\sqrt{49-12z}+7}{2}\text{, }&z\neq 4\text{ and }z\leq \frac{49}{12}\end{matrix}\right.$$