Solve b^2/a+bdiv[(b/a-b)*(ab/a+b)]

$$\frac { b ^ { 2 } } { a + b } \div [ ( \frac { b } { a - b } ) \cdot ( \frac { a b } { a + b } ) ]$$

Evaluate

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

Solution Steps

Multiply \frac{b}{a-b} times \frac{ab}{a+b} by multiplying numerator times numerator and denominator times denominator.

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

Divide \frac{b^{2}}{a+b} by \frac{bab}{\left(a-b\right)\left(a+b\right)} by multiplying \frac{b^{2}}{a+b} by the reciprocal of \frac{bab}{\left(a-b\right)\left(a+b\right)}.

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

Cancel out bb\left(a+b\right) in both numerator and denominator.

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

Differentiate w.r.t. a

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