Solve frac{y^{2}+y-12}{y^{3}+9y^2+20y}divy^2-9/y^3+3y^2

$$\frac { y ^ { 2 } + y - 12 } { y ^ { 3 } + 9 y ^ { 2 } + 20 y } \div \frac { y ^ { 2 } - 9 } { y ^ { 3 } + 3 y ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Divide \frac{y^{2}+y-12}{y^{3}+9y^{2}+20y} by \frac{y^{2}-9}{y^{3}+3y^{2}} by multiplying \frac{y^{2}+y-12}{y^{3}+9y^{2}+20y} by the reciprocal of \frac{y^{2}-9}{y^{3}+3y^{2}}.

$$\frac{\left(y^{2}+y-12\right)\left(y^{3}+3y^{2}\right)}{\left(y^{3}+9y^{2}+20y\right)\left(y^{2}-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-3\right)\left(y+3\right)\left(y+4\right)y^{2}}{y\left(y-3\right)\left(y+3\right)\left(y+4\right)\left(y+5\right)}$$

Cancel out y\left(y-3\right)\left(y+3\right)\left(y+4\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{y^{2}+y-12}{y^{3}+9y^{2}+20y} by \frac{y^{2}-9}{y^{3}+3y^{2}} by multiplying \frac{y^{2}+y-12}{y^{3}+9y^{2}+20y} by the reciprocal of \frac{y^{2}-9}{y^{3}+3y^{2}}.

$$\frac{\left(y^{2}+y-12\right)\left(y^{3}+3y^{2}\right)}{\left(y^{3}+9y^{2}+20y\right)\left(y^{2}-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-3\right)\left(y+3\right)\left(y+4\right)y^{2}}{y\left(y-3\right)\left(y+3\right)\left(y+4\right)\left(y+5\right)}$$

Cancel out y\left(y-3\right)\left(y+3\right)\left(y+4\right) in both numerator and denominator.

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