Solve 2x/3a*18a/xdiv12x/a

$$\frac { 2 x } { 3 a } \times \frac { 18 a } { x } \div \frac { 12 x } { a }$$

Evaluate

$$\frac{a}{x}$$

Solution Steps

Multiply \frac{2x}{3a} times \frac{18a}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2x\times 18a}{3ax}}{\frac{12x}{a}}$$

Cancel out 3ax in both numerator and denominator.

$$\frac{2\times 6}{\frac{12x}{a}}$$

Multiply 2 and 6 to get 12.

$$\frac{12}{\frac{12x}{a}}$$

Divide 12 by \frac{12x}{a} by multiplying 12 by the reciprocal of \frac{12x}{a}.

$$\frac{12a}{12x}$$

Cancel out 12 in both numerator and denominator.

$$\frac{a}{x}$$

Differentiate w.r.t. x

$$-\frac{a}{x^{2}}$$