Solve 4a^2/7b^4:a^5/ab-b^2

$$\frac { 4 a ^ { 2 } } { 7 b ^ { 4 } } : \frac { a ^ { 5 } } { a b - b ^ { 2 } }$$

Evaluate

$$\frac{4\left(a-b\right)}{7\left(ab\right)^{3}}$$

Short Solution Steps

Divide \frac{4a^{2}}{7b^{4}} by \frac{a^{5}}{ab-b^{2}} by multiplying \frac{4a^{2}}{7b^{4}} by the reciprocal of \frac{a^{5}}{ab-b^{2}}.

$$\frac{4a^{2}\left(ab-b^{2}\right)}{7b^{4}a^{5}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{4\left(ab-b^{2}\right)}{7a^{3}b^{4}}$$

Factor the expressions that are not already factored.

$$\frac{4b\left(a-b\right)}{7a^{3}b^{4}}$$

Cancel out b in both numerator and denominator.

$$\frac{4\left(a-b\right)}{7a^{3}b^{3}}$$

Expand the expression.

$$\frac{4a-4b}{7\left(ab\right)^{3}}$$

Expand \left(ab\right)^{3}.

$$\frac{4a-4b}{7a^{3}b^{3}}$$

Differentiate w.r.t. a

$$\frac{4\left(3b-2a\right)}{7b^{3}a^{4}}$$