Solve 4a^2/3b^2:2ax/9b^3

$$\frac { 4 a ^ { 2 } } { 3 b ^ { 2 } } : \frac { 2 a x } { 9 b ^ { 3 } }$$

Evaluate

$$\frac{6ab}{x}$$

Solution Steps

Divide \frac{4a^{2}}{3b^{2}} by \frac{2ax}{9b^{3}} by multiplying \frac{4a^{2}}{3b^{2}} by the reciprocal of \frac{2ax}{9b^{3}}.

$$\frac{4a^{2}\times 9b^{3}}{3b^{2}\times 2ax}$$

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

$$\frac{2\times 3ab}{x}$$

Multiply 2 and 3 to get 6.

$$\frac{6ab}{x}$$

Differentiate w.r.t. x

$$-\frac{6ab}{x^{2}}$$