Solve frac{frac{7ab^{2}}{12c^2d}}{14b^3/3c^4d^3}

$$\frac { \frac { 7 a b ^ { 2 } } { 12 c ^ { 2 } d } } { \frac { 14 b ^ { 3 } } { 3 c ^ { 4 } d ^ { 3 } } }$$

Evaluate

$$\frac{a\left(cd\right)^{2}}{8b}$$

Solution Steps

Divide \frac{7ab^{2}}{12c^{2}d} by \frac{14b^{3}}{3c^{4}d^{3}} by multiplying \frac{7ab^{2}}{12c^{2}d} by the reciprocal of \frac{14b^{3}}{3c^{4}d^{3}}.

$$\frac{7ab^{2}\times 3c^{4}d^{3}}{12c^{2}d\times 14b^{3}}$$

Cancel out 3\times 7db^{2}c^{2} in both numerator and denominator.

$$\frac{ac^{2}d^{2}}{2\times 4b}$$

Multiply 2 and 4 to get 8.

$$\frac{ac^{2}d^{2}}{8b}$$

Differentiate w.r.t. d

$$\frac{adc^{2}}{4b}$$