Solve a/b*2a^2/3b^2div6a^3/4b^2

$$\frac { a } { b } \times \frac { 2 a ^ { 2 } } { 3 b ^ { 2 } } \div \frac { 6 a ^ { 3 } } { 4 b ^ { 2 } }$$

Evaluate

$$\frac{4}{9b}$$

Short Solution Steps

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

$$\frac{\frac{a\times 2a^{2}}{b\times 3b^{2}}}{\frac{6a^{3}}{4b^{2}}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{a\times 2a^{2}}{b\times 3b^{2}}}{\frac{3a^{3}}{2b^{2}}}$$

Divide \frac{a\times 2a^{2}}{b\times 3b^{2}} by \frac{3a^{3}}{2b^{2}} by multiplying \frac{a\times 2a^{2}}{b\times 3b^{2}} by the reciprocal of \frac{3a^{3}}{2b^{2}}.

$$\frac{a\times 2a^{2}\times 2b^{2}}{b\times 3b^{2}\times 3a^{3}}$$

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

$$\frac{2\times 2}{3\times 3b}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3\times 3b}$$

Multiply 3 and 3 to get 9.

$$\frac{4}{9b}$$

Differentiate w.r.t. b

$$-\frac{4}{9b^{2}}$$