Solve frac{3a^{2}b-ab^2}{6a}*9a^2/9a^2-b^2

$$\frac { 3 a ^ { 2 } b - a b ^ { 2 } } { 6 a } \cdot \frac { 9 a ^ { 2 } } { 9 a ^ { 2 } - b ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3a^{2}b-ab^{2}}{6a}.

$$\frac{ab\left(3a-b\right)}{6a}\times \frac{9a^{2}}{9a^{2}-b^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{b\left(3a-b\right)}{6}\times \frac{9a^{2}}{9a^{2}-b^{2}}$$

Multiply \frac{b\left(3a-b\right)}{6} times \frac{9a^{2}}{9a^{2}-b^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b\left(3a-b\right)\times 9a^{2}}{6\left(9a^{2}-b^{2}\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3b\left(3a-b\right)a^{2}}{2\left(9a^{2}-b^{2}\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 3a-b in both numerator and denominator.

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

Expand the expression.

$$\frac{3ba^{2}}{6a+2b}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3a^{2}b-ab^{2}}{6a}.

$$\frac{ab\left(3a-b\right)}{6a}\times \frac{9a^{2}}{9a^{2}-b^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{b\left(3a-b\right)}{6}\times \frac{9a^{2}}{9a^{2}-b^{2}}$$

Multiply \frac{b\left(3a-b\right)}{6} times \frac{9a^{2}}{9a^{2}-b^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b\left(3a-b\right)\times 9a^{2}}{6\left(9a^{2}-b^{2}\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3b\left(3a-b\right)a^{2}}{2\left(9a^{2}-b^{2}\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 3a-b in both numerator and denominator.

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

Expand the expression.

$$\frac{3ba^{2}}{6a+2b}$$