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

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

Solve for y

$$y=3$$

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.

$$\left(y+2\right)\times 4-\left(6y-4\right)=\left(y-2\right)\times 6$$

Use the distributive property to multiply y+2 by 4.

$$4y+8-\left(6y-4\right)=\left(y-2\right)\times 6$$

To find the opposite of 6y-4, find the opposite of each term.

$$4y+8-6y+4=\left(y-2\right)\times 6$$

Combine 4y and -6y to get -2y.

$$-2y+8+4=\left(y-2\right)\times 6$$

Add 8 and 4 to get 12.

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

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

$$-2y+12=6y-12$$

Subtract 6y from both sides.

$$-2y+12-6y=-12$$

Combine -2y and -6y to get -8y.

$$-8y+12=-12$$

Subtract 12 from both sides.

$$-8y=-12-12$$

Subtract 12 from -12 to get -24.

$$-8y=-24$$

Divide both sides by -8.

$$y=\frac{-24}{-8}$$

Divide -24 by -8 to get 3.

$$y=3$$