Solve frac{a^{3}+ba^{2}}{a-b}*a^2-b^2/a^2+2ab+b^2*(1/a+1/b)

$$\frac { a ^ { 3 } + b a ^ { 2 } } { a - b } \cdot \frac { a ^ { 2 } - b ^ { 2 } } { a ^ { 2 } + 2 a b + b ^ { 2 } } \cdot ( \frac { 1 } { a } + \frac { 1 } { b } )$$

Evaluate

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

Short Solution Steps

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

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{\left(a+b\right)\left(a-b\right)}{\left(a+b\right)^{2}}\left(\frac{1}{a}+\frac{1}{b}\right)$$

Cancel out a+b in both numerator and denominator.

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{a-b}{a+b}\left(\frac{1}{a}+\frac{1}{b}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{1}{a} times \frac{b}{b}. Multiply \frac{1}{b} times \frac{a}{a}.

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{a-b}{a+b}\left(\frac{b}{ab}+\frac{a}{ab}\right)$$

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

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{a-b}{a+b}\times \frac{b+a}{ab}$$

Multiply \frac{a^{3}+ba^{2}}{a-b} times \frac{a-b}{a+b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{3}+ba^{2}\right)\left(a-b\right)}{\left(a-b\right)\left(a+b\right)}\times \frac{b+a}{ab}$$

Cancel out a-b in both numerator and denominator.

$$\frac{a^{3}+ba^{2}}{a+b}\times \frac{b+a}{ab}$$

Multiply \frac{a^{3}+ba^{2}}{a+b} times \frac{b+a}{ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{3}+ba^{2}\right)\left(b+a\right)}{\left(a+b\right)ab}$$

Cancel out a+b in both numerator and denominator.

$$\frac{a^{3}+ba^{2}}{ab}$$

Factor the expressions that are not already factored.

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

Cancel out a in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{\left(a+b\right)\left(a-b\right)}{\left(a+b\right)^{2}}\left(\frac{1}{a}+\frac{1}{b}\right)$$

Cancel out a+b in both numerator and denominator.

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{a-b}{a+b}\left(\frac{1}{a}+\frac{1}{b}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{1}{a} times \frac{b}{b}. Multiply \frac{1}{b} times \frac{a}{a}.

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{a-b}{a+b}\left(\frac{b}{ab}+\frac{a}{ab}\right)$$

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

$$\frac{a^{3}+ba^{2}}{a-b}\times \frac{a-b}{a+b}\times \frac{b+a}{ab}$$

Multiply \frac{a^{3}+ba^{2}}{a-b} times \frac{a-b}{a+b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{3}+ba^{2}\right)\left(a-b\right)}{\left(a-b\right)\left(a+b\right)}\times \frac{b+a}{ab}$$

Cancel out a-b in both numerator and denominator.

$$\frac{a^{3}+ba^{2}}{a+b}\times \frac{b+a}{ab}$$

Multiply \frac{a^{3}+ba^{2}}{a+b} times \frac{b+a}{ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{3}+ba^{2}\right)\left(b+a\right)}{\left(a+b\right)ab}$$

Cancel out a+b in both numerator and denominator.

$$\frac{a^{3}+ba^{2}}{ab}$$

Factor the expressions that are not already factored.

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

Cancel out a in both numerator and denominator.

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

Expand the expression.

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