Solve frac{12dn^{3}}{15cd^3}div9c^3n/10c^2d^2

$$\frac { 12 d n ^ { 3 } } { 15 c d ^ { 3 } } \div \frac { 9 c ^ { 3 } n } { 10 c ^ { 2 } d ^ { 2 } }$$

Evaluate

$$\frac{8\times \left(\frac{n}{c}\right)^{2}}{9}$$

Solution Steps

Divide \frac{12dn^{3}}{15cd^{3}} by \frac{9c^{3}n}{10c^{2}d^{2}} by multiplying \frac{12dn^{3}}{15cd^{3}} by the reciprocal of \frac{9c^{3}n}{10c^{2}d^{2}}.

$$\frac{12dn^{3}\times 10c^{2}d^{2}}{15cd^{3}\times 9c^{3}n}$$

Cancel out 3\times 5ccdnd^{2} in both numerator and denominator.

$$\frac{2\times 4n^{2}}{9c^{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{8n^{2}}{9c^{2}}$$

Differentiate w.r.t. n

$$\frac{16n}{9c^{2}}$$