Solve 9y^2/x^2+12x+36div12y/x^2+6x

$$\frac { 9 y ^ { 2 } } { x ^ { 2 } + 12 x + 36 } \div \frac { 12 y } { x ^ { 2 } + 6 x }$$

Evaluate

$$\frac{3xy}{4\left(x+6\right)}$$

Short Solution Steps

Divide \frac{9y^{2}}{x^{2}+12x+36} by \frac{12y}{x^{2}+6x} by multiplying \frac{9y^{2}}{x^{2}+12x+36} by the reciprocal of \frac{12y}{x^{2}+6x}.

$$\frac{9y^{2}\left(x^{2}+6x\right)}{\left(x^{2}+12x+36\right)\times 12y}$$

Cancel out 3y in both numerator and denominator.

$$\frac{3y\left(x^{2}+6x\right)}{4\left(x^{2}+12x+36\right)}$$

Factor the expressions that are not already factored.

$$\frac{3xy\left(x+6\right)}{4\left(x+6\right)^{2}}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{3xy}{4\left(x+6\right)}$$

Expand the expression.

$$\frac{3xy}{4x+24}$$

Differentiate w.r.t. x

$$\frac{9y}{2\left(x+6\right)^{2}}$$