Solve 1/y+4-2/y+2=3/y^2+6y+8

$$\frac { 1 } { y + 4 } - \frac { 2 } { y + 2 } = \frac { 3 } { y ^ { 2 } + 6 y + 8 }$$

Solve for y

$$y=-9$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -4,-2 since division by zero is not defined. Multiply both sides of the equation by \left(y+2\right)\left(y+4\right), the least common multiple of y+4,y+2,y^{2}+6y+8.

$$y+2-\left(y+4\right)\times 2=3$$

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

$$y+2-\left(2y+8\right)=3$$

To find the opposite of 2y+8, find the opposite of each term.

$$y+2-2y-8=3$$

Combine y and -2y to get -y.

$$-y+2-8=3$$

Subtract 8 from 2 to get -6.

$$-y-6=3$$

Add 6 to both sides.

$$-y=3+6$$

Add 3 and 6 to get 9.

$$-y=9$$

Multiply both sides by -1.

$$y=-9$$