Solve a+b/x-1

$$a + \frac { b } { x - 1 }$$

Evaluate

$$\frac{ax+b-a}{x-1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{x-1}{x-1}.

$$\frac{a\left(x-1\right)}{x-1}+\frac{b}{x-1}$$

Since \frac{a\left(x-1\right)}{x-1} and \frac{b}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{a\left(x-1\right)+b}{x-1}$$

Do the multiplications in a\left(x-1\right)+b.

$$\frac{ax-a+b}{x-1}$$

Differentiate w.r.t. x

$$-\frac{b}{\left(x-1\right)^{2}}$$