Solve 2a-b/a+b+a(b-a)/a^2+2ab+b^2=

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

Evaluate

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

Short Solution Steps

Factor a^{2}+2ab+b^{2}.

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

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

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

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

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

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

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

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

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

Expand \left(a+b\right)^{2}.

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

Expand

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

Short Solution Steps

Factor a^{2}+2ab+b^{2}.

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

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

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

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

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

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

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

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

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

Expand \left(a+b\right)^{2}.

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