Solve 5/y-2-2y-2/y^2-4=6/y+2

$$\frac { 5 } { y - 2 } - \frac { 2 y - 2 } { y ^ { 2 } - 4 } = \frac { 6 } { y + 2 }$$

Solve for y

$$y=8$$

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}-4,y+2.

$$\left(y+2\right)\times 5-\left(2y-2\right)=\left(y-2\right)\times 6$$

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

$$5y+10-\left(2y-2\right)=\left(y-2\right)\times 6$$

To find the opposite of 2y-2, find the opposite of each term.

$$5y+10-2y+2=\left(y-2\right)\times 6$$

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

$$3y+10+2=\left(y-2\right)\times 6$$

Add 10 and 2 to get 12.

$$3y+12=\left(y-2\right)\times 6$$

Use the distributive property to multiply y-2 by 6.

$$3y+12=6y-12$$

Subtract 6y from both sides.

$$3y+12-6y=-12$$

Combine 3y and -6y to get -3y.

$$-3y+12=-12$$

Subtract 12 from both sides.

$$-3y=-12-12$$

Subtract 12 from -12 to get -24.

$$-3y=-24$$

Divide both sides by -3.

$$y=\frac{-24}{-3}$$

Divide -24 by -3 to get 8.

$$y=8$$