Solve 3y+18/y^2*4y/6y+36

$$\frac { 3 y + 18 } { y ^ { 2 } } \cdot \frac { 4 y } { 6 y + 36 }$$

Evaluate

$$\frac{2}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4y}{6y+36}.

$$\frac{3y+18}{y^{2}}\times \frac{4y}{6\left(y+6\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3y+18}{y^{2}}\times \frac{2y}{3\left(y+6\right)}$$

Multiply \frac{3y+18}{y^{2}} times \frac{2y}{3\left(y+6\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3y+18\right)\times 2y}{y^{2}\times 3\left(y+6\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{2\left(3y+18\right)}{3y\left(y+6\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 3\left(y+6\right) in both numerator and denominator.

$$\frac{2}{y}$$

Expand

$$\frac{2}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4y}{6y+36}.

$$\frac{3y+18}{y^{2}}\times \frac{4y}{6\left(y+6\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3y+18}{y^{2}}\times \frac{2y}{3\left(y+6\right)}$$

Multiply \frac{3y+18}{y^{2}} times \frac{2y}{3\left(y+6\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3y+18\right)\times 2y}{y^{2}\times 3\left(y+6\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{2\left(3y+18\right)}{3y\left(y+6\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 3\left(y+6\right) in both numerator and denominator.

$$\frac{2}{y}$$