Solve 9/y+2-5/y-2=8/y^2-4

$$\frac { 9 } { y + 2 } - \frac { 5 } { y - 2 } = \frac { 8 } { y ^ { 2 } - 4 }$$

Solve for y

$$y=9$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(y-2\right)\left(y+2\right), the least common multiple of y+2,y-2,y^{2}-4.

$$\left(y-2\right)\times 9-\left(y+2\right)\times 5=8$$

Use the distributive property to multiply y-2 by 9.

$$9y-18-\left(y+2\right)\times 5=8$$

Use the distributive property to multiply y+2 by 5.

$$9y-18-\left(5y+10\right)=8$$

To find the opposite of 5y+10, find the opposite of each term.

$$9y-18-5y-10=8$$

Combine 9y and -5y to get 4y.

$$4y-18-10=8$$

Subtract 10 from -18 to get -28.

$$4y-28=8$$

Add 28 to both sides.

$$4y=8+28$$

Add 8 and 28 to get 36.

$$4y=36$$

Divide both sides by 4.

$$y=\frac{36}{4}$$

Divide 36 by 4 to get 9.

$$y=9$$