Solve ab/6c^2div2b^2/a*8ac/a^2b

$$\frac { a b } { 6 c ^ { 2 } } \div \frac { 2 b ^ { 2 } } { a } \times \frac { 8 a c } { a ^ { 2 } b }$$

Evaluate

$$\frac{2a}{3cb^{2}}$$

Solution Steps

Divide \frac{ab}{6c^{2}} by \frac{2b^{2}}{a} by multiplying \frac{ab}{6c^{2}} by the reciprocal of \frac{2b^{2}}{a}.

$$\frac{aba}{6c^{2}\times 2b^{2}}\times \frac{8ac}{a^{2}b}$$

Cancel out b in both numerator and denominator.

$$\frac{aa}{2\times 6bc^{2}}\times \frac{8ac}{a^{2}b}$$

Multiply a and a to get a^{2}.

$$\frac{a^{2}}{2\times 6bc^{2}}\times \frac{8ac}{a^{2}b}$$

Multiply 2 and 6 to get 12.

$$\frac{a^{2}}{12bc^{2}}\times \frac{8ac}{a^{2}b}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{2}}{12bc^{2}}\times \frac{8c}{ab}$$

Multiply \frac{a^{2}}{12bc^{2}} times \frac{8c}{ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{2}\times 8c}{12bc^{2}ab}$$

Cancel out 4ac in both numerator and denominator.

$$\frac{2a}{3bbc}$$

Multiply b and b to get b^{2}.

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

Differentiate w.r.t. b

$$-\frac{4a}{3cb^{3}}$$