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

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

Evaluate

$$\frac{\left(a+b\right)\left(a+b+1\right)}{a}$$

Short Solution Steps

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

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

Cancel out a-b in both numerator and denominator.

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

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

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

Since \frac{a+b}{a} and \frac{aa}{a} have the same denominator, add them by adding their numerators.

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

Do the multiplications in a+b+aa.

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

Since \frac{a+b+a^{2}}{a} and \frac{2ab+b^{2}}{a} have the same denominator, add them by adding their numerators.

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

Expand

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

Short Solution Steps

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

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

Cancel out a-b in both numerator and denominator.

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

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

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

Since \frac{a+b}{a} and \frac{aa}{a} have the same denominator, add them by adding their numerators.

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

Do the multiplications in a+b+aa.

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

Since \frac{a+b+a^{2}}{a} and \frac{2ab+b^{2}}{a} have the same denominator, add them by adding their numerators.

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