Solve 2/4+y=1/4-y+3/y

$$\frac { 2 } { 4 + y } = \frac { 1 } { 4 - y } + \frac { 3 } { y }$$

Solve for y

$$y=12$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -4,0,4 since division by zero is not defined. Multiply both sides of the equation by y\left(y-4\right)\left(y+4\right), the least common multiple of 4+y,4-y,y.

$$y\left(y-4\right)\times 2=-y\left(4+y\right)+\left(y^{2}-16\right)\times 3$$

Use the distributive property to multiply y by y-4.

$$\left(y^{2}-4y\right)\times 2=-y\left(4+y\right)+\left(y^{2}-16\right)\times 3$$

Use the distributive property to multiply y^{2}-4y by 2.

$$2y^{2}-8y=-y\left(4+y\right)+\left(y^{2}-16\right)\times 3$$

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

$$2y^{2}-8y=-4y-y^{2}+\left(y^{2}-16\right)\times 3$$

Use the distributive property to multiply y^{2}-16 by 3.

$$2y^{2}-8y=-4y-y^{2}+3y^{2}-48$$

Combine -y^{2} and 3y^{2} to get 2y^{2}.

$$2y^{2}-8y=-4y+2y^{2}-48$$

Add 4y to both sides.

$$2y^{2}-8y+4y=2y^{2}-48$$

Combine -8y and 4y to get -4y.

$$2y^{2}-4y=2y^{2}-48$$

Subtract 2y^{2} from both sides.

$$2y^{2}-4y-2y^{2}=-48$$

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

$$-4y=-48$$

Divide both sides by -4.

$$y=\frac{-48}{-4}$$

Divide -48 by -4 to get 12.

$$y=12$$