Solve 2x/ax+6/frac{3y{ay+6y}}

$$\frac{ \frac{ 2x }{ ax+6 } }{ \frac{ 3y }{ ay+6y } }$$

Evaluate

$$\frac{2x\left(a+6\right)}{3\left(ax+6\right)}$$

Short Solution Steps

Divide \frac{2x}{ax+6} by \frac{3y}{ay+6y} by multiplying \frac{2x}{ax+6} by the reciprocal of \frac{3y}{ay+6y}.

$$\frac{2x\left(ay+6y\right)}{\left(ax+6\right)\times 3y}$$

Factor the expressions that are not already factored.

$$\frac{2xy\left(a+6\right)}{3y\left(ax+6\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{2x\left(a+6\right)}{3\left(ax+6\right)}$$

Expand the expression.

$$\frac{2ax+12x}{3ax+18}$$

Differentiate w.r.t. x

$$\frac{4\left(a+6\right)}{\left(ax+6\right)^{2}}$$