Solve frac{y^{2}-y-56}{2y^2-7y-72}*2y^2+13y+18/y^2+9y+14div2y+y^2/5+y

$$\frac { y ^ { 2 } - y - 56 } { 2 y ^ { 2 } - 7 y - 72 } \cdot \frac { 2 y ^ { 2 } + 13 y + 18 } { y ^ { 2 } + 9 y + 14 } \div \frac { 2 y + y ^ { 2 } } { 5 + y }$$

Evaluate

$$\frac{y+5}{y\left(y+2\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-y-56}{2y^{2}-7y-72}.

$$\frac{\frac{\left(y-8\right)\left(y+7\right)}{\left(y-8\right)\left(2y+9\right)}\times \frac{2y^{2}+13y+18}{y^{2}+9y+14}}{\frac{2y+y^{2}}{5+y}}$$

Cancel out y-8 in both numerator and denominator.

$$\frac{\frac{y+7}{2y+9}\times \frac{2y^{2}+13y+18}{y^{2}+9y+14}}{\frac{2y+y^{2}}{5+y}}$$

Factor the expressions that are not already factored in \frac{2y^{2}+13y+18}{y^{2}+9y+14}.

$$\frac{\frac{y+7}{2y+9}\times \frac{\left(y+2\right)\left(2y+9\right)}{\left(y+2\right)\left(y+7\right)}}{\frac{2y+y^{2}}{5+y}}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{\frac{y+7}{2y+9}\times \frac{2y+9}{y+7}}{\frac{2y+y^{2}}{5+y}}$$

Multiply \frac{y+7}{2y+9} times \frac{2y+9}{y+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(y+7\right)\left(2y+9\right)}{\left(2y+9\right)\left(y+7\right)}}{\frac{2y+y^{2}}{5+y}}$$

Cancel out \left(y+7\right)\left(2y+9\right) in both numerator and denominator.

$$\frac{1}{\frac{2y+y^{2}}{5+y}}$$

Divide 1 by \frac{2y+y^{2}}{5+y} by multiplying 1 by the reciprocal of \frac{2y+y^{2}}{5+y}.

$$\frac{5+y}{2y+y^{2}}$$

Expand

$$\frac{y+5}{y\left(y+2\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-y-56}{2y^{2}-7y-72}.

$$\frac{\frac{\left(y-8\right)\left(y+7\right)}{\left(y-8\right)\left(2y+9\right)}\times \frac{2y^{2}+13y+18}{y^{2}+9y+14}}{\frac{2y+y^{2}}{5+y}}$$

Cancel out y-8 in both numerator and denominator.

$$\frac{\frac{y+7}{2y+9}\times \frac{2y^{2}+13y+18}{y^{2}+9y+14}}{\frac{2y+y^{2}}{5+y}}$$

Factor the expressions that are not already factored in \frac{2y^{2}+13y+18}{y^{2}+9y+14}.

$$\frac{\frac{y+7}{2y+9}\times \frac{\left(y+2\right)\left(2y+9\right)}{\left(y+2\right)\left(y+7\right)}}{\frac{2y+y^{2}}{5+y}}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{\frac{y+7}{2y+9}\times \frac{2y+9}{y+7}}{\frac{2y+y^{2}}{5+y}}$$

Multiply \frac{y+7}{2y+9} times \frac{2y+9}{y+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(y+7\right)\left(2y+9\right)}{\left(2y+9\right)\left(y+7\right)}}{\frac{2y+y^{2}}{5+y}}$$

Cancel out \left(y+7\right)\left(2y+9\right) in both numerator and denominator.

$$\frac{1}{\frac{2y+y^{2}}{5+y}}$$

Divide 1 by \frac{2y+y^{2}}{5+y} by multiplying 1 by the reciprocal of \frac{2y+y^{2}}{5+y}.

$$\frac{5+y}{2y+y^{2}}$$