Solve a^2+ab/ab+b^2+2ab/ab-b^2

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

Evaluate

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

Short Solution Steps

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

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

Cancel out a+b in both numerator and denominator.

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

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

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

Cancel out b in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a-b is b\left(a-b\right). Multiply \frac{a}{b} times \frac{a-b}{a-b}. Multiply \frac{2a}{a-b} times \frac{b}{b}.

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

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

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

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

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

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

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

Expand b\left(a-b\right).

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

Expand

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

Short Solution Steps

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

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

Cancel out a+b in both numerator and denominator.

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

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

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

Cancel out b in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a-b is b\left(a-b\right). Multiply \frac{a}{b} times \frac{a-b}{a-b}. Multiply \frac{2a}{a-b} times \frac{b}{b}.

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

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

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

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

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

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

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

Expand b\left(a-b\right).

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