Solve y+1/y-6+y+3y+2/y^2-4y-12-y^2-5y-6/y^2-12y+36

$$\frac { y + 1 } { y - 6 } + \frac { y + 3 y + 2 } { y ^ { 2 } - 4 y - 12 } - \frac { y ^ { 2 } - 5 y - 6 } { y ^ { 2 } - 12 y + 36 }$$

Evaluate

$$\frac{2\left(2y+1\right)}{\left(y-6\right)\left(y+2\right)}$$

Short Solution Steps

Combine y and 3y to get 4y.

$$\frac{y+1}{y-6}+\frac{4y+2}{y^{2}-4y-12}-\frac{y^{2}-5y-6}{y^{2}-12y+36}$$

Factor the expressions that are not already factored in \frac{y^{2}-5y-6}{y^{2}-12y+36}.

$$\frac{y+1}{y-6}+\frac{4y+2}{y^{2}-4y-12}-\frac{\left(y-6\right)\left(y+1\right)}{\left(y-6\right)^{2}}$$

Cancel out y-6 in both numerator and denominator.

$$\frac{y+1}{y-6}+\frac{4y+2}{y^{2}-4y-12}-\frac{y+1}{y-6}$$

Subtract \frac{y+1}{y-6} from \frac{y+1}{y-6} to get 0.

$$\frac{4y+2}{y^{2}-4y-12}$$

Expand

$$\frac{2\left(2y+1\right)}{y^{2}-4y-12}$$

Short Solution Steps

Combine y and 3y to get 4y.

$$\frac{y+1}{y-6}+\frac{4y+2}{y^{2}-4y-12}-\frac{y^{2}-5y-6}{y^{2}-12y+36}$$

Factor the expressions that are not already factored in \frac{y^{2}-5y-6}{y^{2}-12y+36}.

$$\frac{y+1}{y-6}+\frac{4y+2}{y^{2}-4y-12}-\frac{\left(y-6\right)\left(y+1\right)}{\left(y-6\right)^{2}}$$

Cancel out y-6 in both numerator and denominator.

$$\frac{y+1}{y-6}+\frac{4y+2}{y^{2}-4y-12}-\frac{y+1}{y-6}$$

Subtract \frac{y+1}{y-6} from \frac{y+1}{y-6} to get 0.

$$\frac{4y+2}{y^{2}-4y-12}$$