Solve ab^2/2c^3div3a^2b^2/-4c

$$\frac { a b ^ { 2 } } { 2 c ^ { 3 } } \div \frac { 3 a ^ { 2 } b ^ { 2 } } { - 4 c }$$

Evaluate

$$-\frac{2}{3ac^{2}}$$

Solution Steps

Divide \frac{ab^{2}}{2c^{3}} by \frac{3a^{2}b^{2}}{-4c} by multiplying \frac{ab^{2}}{2c^{3}} by the reciprocal of \frac{3a^{2}b^{2}}{-4c}.

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

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

$$\frac{-2}{3ac^{2}}$$

Differentiate w.r.t. a

$$\frac{2}{3\left(ac\right)^{2}}$$