Solve 3a-b/a^{3-b^{3}}*a^2+ab+b^2/3a^2-4ab+b^2

$$\frac { 3 a - b } { a ^ { 3 } - b ^ { 3 } } \cdot \frac { a ^ { 2 } + a b + b ^ { 2 } } { 3 a ^ { 2 } - 4 a b + b ^ { 2 } }$$

Evaluate

$$\frac{1}{\left(a-b\right)^{2}}$$

Short Solution Steps

Multiply \frac{3a-b}{a^{3}-b^{3}} times \frac{a^{2}+ab+b^{2}}{3a^{2}-4ab+b^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3a-b\right)\left(a^{2}+ab+b^{2}\right)}{\left(a^{3}-b^{3}\right)\left(3a^{2}-4ab+b^{2}\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(3a-b\right)\left(a^{2}+ab+b^{2}\right) in both numerator and denominator.

$$\frac{1}{\left(a-b\right)^{2}}$$

Expand the expression.

$$\frac{1}{a^{2}-2ab+b^{2}}$$

Expand

$$\frac{1}{\left(a-b\right)^{2}}$$

Short Solution Steps

Multiply \frac{3a-b}{a^{3}-b^{3}} times \frac{a^{2}+ab+b^{2}}{3a^{2}-4ab+b^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3a-b\right)\left(a^{2}+ab+b^{2}\right)}{\left(a^{3}-b^{3}\right)\left(3a^{2}-4ab+b^{2}\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(3a-b\right)\left(a^{2}+ab+b^{2}\right) in both numerator and denominator.

$$\frac{1}{\left(a-b\right)^{2}}$$

Expand the expression.

$$\frac{1}{a^{2}-2ab+b^{2}}$$