Solve y^2+17/y^2-1=y-2/y+1-5/1-y

$$\frac { y ^ { 2 } + 17 } { y ^ { 2 } - 1 } = \frac { y - 2 } { y + 1 } - \frac { 5 } { 1 - y }$$

Solve for y

$$y=5$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(y-1\right)\left(y+1\right), the least common multiple of y^{2}-1,y+1,1-y.

$$y^{2}+17=\left(y-1\right)\left(y-2\right)-\left(-\left(1+y\right)\times 5\right)$$

Use the distributive property to multiply y-1 by y-2 and combine like terms.

$$y^{2}+17=y^{2}-3y+2-\left(-\left(1+y\right)\times 5\right)$$

Multiply -1 and 5 to get -5.

$$y^{2}+17=y^{2}-3y+2-\left(-5\left(1+y\right)\right)$$

Use the distributive property to multiply -5 by 1+y.

$$y^{2}+17=y^{2}-3y+2-\left(-5-5y\right)$$

To find the opposite of -5-5y, find the opposite of each term.

$$y^{2}+17=y^{2}-3y+2+5+5y$$

Add 2 and 5 to get 7.

$$y^{2}+17=y^{2}-3y+7+5y$$

Combine -3y and 5y to get 2y.

$$y^{2}+17=y^{2}+2y+7$$

Subtract y^{2} from both sides.

$$y^{2}+17-y^{2}=2y+7$$

Combine y^{2} and -y^{2} to get 0.

$$17=2y+7$$

Swap sides so that all variable terms are on the left hand side.

$$2y+7=17$$

Subtract 7 from both sides.

$$2y=17-7$$

Subtract 7 from 17 to get 10.

$$2y=10$$

Divide both sides by 2.

$$y=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$y=5$$