Solve 1/1-frac{a{b}}

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

Evaluate

$$\frac{b}{b-a}$$

Solution Steps

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

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

Since \frac{b}{b} and \frac{a}{b} have the same denominator, subtract them by subtracting their numerators.

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

Divide 1 by \frac{b-a}{b} by multiplying 1 by the reciprocal of \frac{b-a}{b}.

$$\frac{b}{b-a}$$

Differentiate w.r.t. b

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