Solve 10/2y+8-7y+8/y^2-16=-8/2y-8

$$\frac { 10 } { 2 y + 8 } - \frac { 7 y + 8 } { y ^ { 2 } - 16 } = \frac { - 8 } { 2 y - 8 }$$

Solve for y

$$y=6$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -4,4 since division by zero is not defined. Multiply both sides of the equation by 2\left(y-4\right)\left(y+4\right), the least common multiple of 2y+8,y^{2}-16,2y-8.

$$\left(y-4\right)\times 10-2\left(7y+8\right)=\left(y+4\right)\left(-8\right)$$

Use the distributive property to multiply y-4 by 10.

$$10y-40-2\left(7y+8\right)=\left(y+4\right)\left(-8\right)$$

Use the distributive property to multiply -2 by 7y+8.

$$10y-40-14y-16=\left(y+4\right)\left(-8\right)$$

Combine 10y and -14y to get -4y.

$$-4y-40-16=\left(y+4\right)\left(-8\right)$$

Subtract 16 from -40 to get -56.

$$-4y-56=\left(y+4\right)\left(-8\right)$$

Use the distributive property to multiply y+4 by -8.

$$-4y-56=-8y-32$$

Add 8y to both sides.

$$-4y-56+8y=-32$$

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

$$4y-56=-32$$

Add 56 to both sides.

$$4y=-32+56$$

Add -32 and 56 to get 24.

$$4y=24$$

Divide both sides by 4.

$$y=\frac{24}{4}$$

Divide 24 by 4 to get 6.

$$y=6$$