Solve (a+2ab/a-b)diva+b/a-b

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

Evaluate

$$a$$

Short Solution Steps

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

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

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

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

Do the multiplications in a\left(a-b\right)+2ab.

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

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

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

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

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

Cancel out a-b in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a+b 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 times \frac{a-b}{a-b}.

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

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

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

Do the multiplications in a\left(a-b\right)+2ab.

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

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

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

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

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

Cancel out a-b in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{a^{2}+ab}{a+b}.

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

Cancel out a+b 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.

$$1$$