Solve 2x+6y/6x^2*9x^3/x^2+6xy+9y^2

$$\frac { 2 x + 6 y } { 6 x ^ { 2 } } \times \frac { 9 x ^ { 3 } } { x ^ { 2 } + 6 x y + 9 y ^ { 2 } }$$

Evaluate

$$\frac{3x}{x+3y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+6y}{6x^{2}}.

$$\frac{2\left(x+3y\right)}{6x^{2}}\times \frac{9x^{3}}{x^{2}+6xy+9y^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x+3y}{3x^{2}}\times \frac{9x^{3}}{x^{2}+6xy+9y^{2}}$$

Multiply \frac{x+3y}{3x^{2}} times \frac{9x^{3}}{x^{2}+6xy+9y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3y\right)\times 9x^{3}}{3x^{2}\left(x^{2}+6xy+9y^{2}\right)}$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{3x\left(x+3y\right)}{x^{2}+6xy+9y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{3x\left(x+3y\right)}{\left(x+3y\right)^{2}}$$

Cancel out x+3y in both numerator and denominator.

$$\frac{3x}{x+3y}$$

Expand

$$\frac{3x}{x+3y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+6y}{6x^{2}}.

$$\frac{2\left(x+3y\right)}{6x^{2}}\times \frac{9x^{3}}{x^{2}+6xy+9y^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x+3y}{3x^{2}}\times \frac{9x^{3}}{x^{2}+6xy+9y^{2}}$$

Multiply \frac{x+3y}{3x^{2}} times \frac{9x^{3}}{x^{2}+6xy+9y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3y\right)\times 9x^{3}}{3x^{2}\left(x^{2}+6xy+9y^{2}\right)}$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{3x\left(x+3y\right)}{x^{2}+6xy+9y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{3x\left(x+3y\right)}{\left(x+3y\right)^{2}}$$

Cancel out x+3y in both numerator and denominator.

$$\frac{3x}{x+3y}$$