Solve a+b/a=2(a-1)

$$\frac { a + b } { a } = 2 ( a - 1 )$$

Solve for b

$$b=-a\left(3-2a\right)$$

$$a\neq 0$$

Solution Steps

Multiply both sides of the equation by a.

$$a+b=2\left(a-1\right)a$$

Use the distributive property to multiply 2 by a-1.

$$a+b=\left(2a-2\right)a$$

Use the distributive property to multiply 2a-2 by a.

$$a+b=2a^{2}-2a$$

Subtract a from both sides.

$$b=2a^{2}-2a-a$$

Combine -2a and -a to get -3a.

$$b=2a^{2}-3a$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\sqrt{8b+9}+3}{4}\text{, }&b\geq -\frac{9}{8}\\a=\frac{-\sqrt{8b+9}+3}{4}\text{, }&b\neq 0\text{ and }b\geq -\frac{9}{8}\end{matrix}\right.$$