Solve (a-b+b^2/a+b)*a+b/a

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

Evaluate

$$a$$

Short Solution Steps

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

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

Since \frac{\left(a-b\right)\left(a+b\right)}{a+b} and \frac{b^{2}}{a+b} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(a-b\right)\left(a+b\right)+b^{2}.

$$\frac{a^{2}+ab-ba-b^{2}+b^{2}}{a+b}\times \frac{a+b}{a}$$

Combine like terms in a^{2}+ab-ba-b^{2}+b^{2}.

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

Multiply \frac{a^{2}}{a+b} times \frac{a+b}{a} by multiplying numerator times numerator and denominator times denominator.

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

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

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

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

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

Since \frac{\left(a-b\right)\left(a+b\right)}{a+b} and \frac{b^{2}}{a+b} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(a-b\right)\left(a+b\right)+b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}+ab-ba-b^{2}+b^{2}}{a+b}\times \frac{a+b}{a})$$

Combine like terms in a^{2}+ab-ba-b^{2}+b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{a+b}\times \frac{a+b}{a})$$

Multiply \frac{a^{2}}{a+b} times \frac{a+b}{a} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a)$$

The derivative of ax^{n} is nax^{n-1}.

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

For any term t except 0, t^{0}=1.

$$1$$