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

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

Solve for y

$$y=4$$

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.

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

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

$$2y+4-2=\left(y-2\right)\times 5$$

Subtract 2 from 4 to get 2.

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

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

$$2y+2=5y-10$$

Subtract 5y from both sides.

$$2y+2-5y=-10$$

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

$$-3y+2=-10$$

Subtract 2 from both sides.

$$-3y=-10-2$$

Subtract 2 from -10 to get -12.

$$-3y=-12$$

Divide both sides by -3.

$$y=\frac{-12}{-3}$$

Divide -12 by -3 to get 4.

$$y=4$$