Solve y/y+3y^2+7y+12/4y^2

$$\frac{ y }{ y+3 } \frac{ { y }^{ 2 } +7y+12 }{ 4 { y }^{ 2 } }$$

Evaluate

$$\frac{1}{4}+\frac{1}{y}$$

Short Solution Steps

Multiply \frac{y}{y+3} times \frac{y^{2}+7y+12}{4y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y\left(y^{2}+7y+12\right)}{\left(y+3\right)\times 4y^{2}}$$

Cancel out y in both numerator and denominator.

$$\frac{y^{2}+7y+12}{4y\left(y+3\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y+3\right)\left(y+4\right)}{4y\left(y+3\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y+4}{4y}$$

Expand

$$\frac{1}{4}+\frac{1}{y}$$

Short Solution Steps

Multiply \frac{y}{y+3} times \frac{y^{2}+7y+12}{4y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y\left(y^{2}+7y+12\right)}{\left(y+3\right)\times 4y^{2}}$$

Cancel out y in both numerator and denominator.

$$\frac{y^{2}+7y+12}{4y\left(y+3\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y+3\right)\left(y+4\right)}{4y\left(y+3\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y+4}{4y}$$