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

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

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}.

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

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

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

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

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

Combine like terms in a-a+b.

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

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

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