Solve frac{3n^{2}-2ny-y^{2}+3y^{2}-n^{2}-2ny}{n^3+y^3-n^2y-ny^2}

$$\frac { 3 n ^ { 2 } - 2 n y - y ^ { 2 } + 3 y ^ { 2 } - n ^ { 2 } - 2 n y } { n ^ { 3 } + y ^ { 3 } - n ^ { 2 } y - n y ^ { 2 } }$$

Evaluate

$$\frac{2}{y+n}$$

Short Solution Steps

Combine -y^{2} and 3y^{2} to get 2y^{2}.

$$\frac{3n^{2}-2ny+2y^{2}-n^{2}-2ny}{n^{3}+y^{3}-n^{2}y-ny^{2}}$$

Combine 3n^{2} and -n^{2} to get 2n^{2}.

$$\frac{2n^{2}-2ny+2y^{2}-2ny}{n^{3}+y^{3}-n^{2}y-ny^{2}}$$

Combine -2ny and -2ny to get -4ny.

$$\frac{2n^{2}-4ny+2y^{2}}{n^{3}+y^{3}-n^{2}y-ny^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\left(-y+n\right)^{2}}{\left(y+n\right)\left(-y+n\right)^{2}}$$

Cancel out \left(-y+n\right)^{2} in both numerator and denominator.

$$\frac{2}{y+n}$$

Expand

$$\frac{2}{y+n}$$

Short Solution Steps

Combine -y^{2} and 3y^{2} to get 2y^{2}.

$$\frac{3n^{2}-2ny+2y^{2}-n^{2}-2ny}{n^{3}+y^{3}-n^{2}y-ny^{2}}$$

Combine 3n^{2} and -n^{2} to get 2n^{2}.

$$\frac{2n^{2}-2ny+2y^{2}-2ny}{n^{3}+y^{3}-n^{2}y-ny^{2}}$$

Combine -2ny and -2ny to get -4ny.

$$\frac{2n^{2}-4ny+2y^{2}}{n^{3}+y^{3}-n^{2}y-ny^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\left(-y+n\right)^{2}}{\left(y+n\right)\left(-y+n\right)^{2}}$$

Cancel out \left(-y+n\right)^{2} in both numerator and denominator.

$$\frac{2}{y+n}$$