Solve frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^2}*a^2-ab/4a^3+20a^2b

$$\frac { 2 a ^ { 2 } + 9 a b - 5 b ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \cdot \frac { a ^ { 2 } - a b } { 4 a ^ { 3 } + 20 a ^ { 2 } b }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-ab}{4a^{3}+20a^{2}b}.

$$\frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^{2}}\times \frac{a\left(a-b\right)}{4\left(a+5b\right)a^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^{2}}\times \frac{a-b}{4a\left(a+5b\right)}$$

Multiply \frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^{2}} times \frac{a-b}{4a\left(a+5b\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2a^{2}+9ab-5b^{2}\right)\left(a-b\right)}{\left(a^{2}-b^{2}\right)\times 4a\left(a+5b\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-b\right)\left(a+5b\right)\left(2a-b\right)}{4a\left(a+b\right)\left(a-b\right)\left(a+5b\right)}$$

Cancel out \left(a-b\right)\left(a+5b\right) in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-ab}{4a^{3}+20a^{2}b}.

$$\frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^{2}}\times \frac{a\left(a-b\right)}{4\left(a+5b\right)a^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^{2}}\times \frac{a-b}{4a\left(a+5b\right)}$$

Multiply \frac{2a^{2}+9ab-5b^{2}}{a^{2}-b^{2}} times \frac{a-b}{4a\left(a+5b\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2a^{2}+9ab-5b^{2}\right)\left(a-b\right)}{\left(a^{2}-b^{2}\right)\times 4a\left(a+5b\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-b\right)\left(a+5b\right)\left(2a-b\right)}{4a\left(a+b\right)\left(a-b\right)\left(a+5b\right)}$$

Cancel out \left(a-b\right)\left(a+5b\right) in both numerator and denominator.

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

Expand the expression.

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