Solve frac{(a-b)^{3}}{a^{3}-b^3}*a^2-b^2/(a-b)^2

$$\frac { ( a - b ) ^ { 3 } } { a ^ { 3 } - b ^ { 3 } } \times \frac { a ^ { 2 } - b ^ { 2 } } { ( a - b ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(a-b\right)^{3}}{a^{3}-b^{3}}.

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

Cancel out a-b in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{a^{2}-b^{2}}{\left(a-b\right)^{2}}.

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

Cancel out a-b in both numerator and denominator.

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

Multiply \frac{\left(a-b\right)^{2}}{a^{2}+ab+b^{2}} times \frac{a+b}{a-b} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a-b in both numerator and denominator.

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

Consider \left(a+b\right)\left(a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(a-b\right)^{3}}{a^{3}-b^{3}}.

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

Cancel out a-b in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{a^{2}-b^{2}}{\left(a-b\right)^{2}}.

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

Cancel out a-b in both numerator and denominator.

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

Multiply \frac{\left(a-b\right)^{2}}{a^{2}+ab+b^{2}} times \frac{a+b}{a-b} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a-b in both numerator and denominator.

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

Consider \left(a+b\right)\left(a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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