Solve 6ab/4bcdiv2ab^2/8bc^2*bc^2/b^2c

$$\frac{ 6ab }{ 4bc } \div \frac{ 2a { b }^{ 2 } }{ 8b { c }^{ 2 } } \times \frac{ b { c }^{ 2 } }{ { b }^{ 2 } c }$$

Evaluate

$$6\times \left(\frac{c}{b}\right)^{2}$$

Solution Steps

Divide \frac{6ab}{4bc} by \frac{2ab^{2}}{8bc^{2}} by multiplying \frac{6ab}{4bc} by the reciprocal of \frac{2ab^{2}}{8bc^{2}}.

$$\frac{6ab\times 8bc^{2}}{4bc\times 2ab^{2}}\times \frac{bc^{2}}{b^{2}c}$$

Cancel out 2\times 2\times 2abbc in both numerator and denominator.

$$\frac{2\times 3c}{b}\times \frac{bc^{2}}{b^{2}c}$$

Multiply 2 and 3 to get 6.

$$\frac{6c}{b}\times \frac{bc^{2}}{b^{2}c}$$

Cancel out bc in both numerator and denominator.

$$\frac{6c}{b}\times \frac{c}{b}$$

Multiply \frac{6c}{b} times \frac{c}{b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6cc}{bb}$$

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

$$\frac{6c^{2}}{bb}$$

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

$$\frac{6c^{2}}{b^{2}}$$

Differentiate w.r.t. c

$$\frac{12c}{b^{2}}$$