Solve b/a^2-b^2div(1-a/a+b)

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

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{b}{a^{2}-b^{2}}}{\frac{a+b}{a+b}-\frac{a}{a+b}}$$

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

$$\frac{\frac{b}{a^{2}-b^{2}}}{\frac{a+b-a}{a+b}}$$

Combine like terms in a+b-a.

$$\frac{\frac{b}{a^{2}-b^{2}}}{\frac{b}{a+b}}$$

Divide \frac{b}{a^{2}-b^{2}} by \frac{b}{a+b} by multiplying \frac{b}{a^{2}-b^{2}} by the reciprocal of \frac{b}{a+b}.

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

Cancel out b in both numerator and denominator.

$$\frac{a+b}{a^{2}-b^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out a+b in both numerator and denominator.

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

Differentiate w.r.t. a

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