Solve 2y/y^2-9+5/y-3=4/y+3

$$\frac { 2 y } { y ^ { 2 } - 9 } + \frac { 5 } { y - 3 } = \frac { 4 } { y + 3 }$$

Solve for y

$$y=-9$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(y-3\right)\left(y+3\right), the least common multiple of y^{2}-9,y-3,y+3.

$$2y+\left(y+3\right)\times 5=\left(y-3\right)\times 4$$

Use the distributive property to multiply y+3 by 5.

$$2y+5y+15=\left(y-3\right)\times 4$$

Combine 2y and 5y to get 7y.

$$7y+15=\left(y-3\right)\times 4$$

Use the distributive property to multiply y-3 by 4.

$$7y+15=4y-12$$

Subtract 4y from both sides.

$$7y+15-4y=-12$$

Combine 7y and -4y to get 3y.

$$3y+15=-12$$

Subtract 15 from both sides.

$$3y=-12-15$$

Subtract 15 from -12 to get -27.

$$3y=-27$$

Divide both sides by 3.

$$y=\frac{-27}{3}$$

Divide -27 by 3 to get -9.

$$y=-9$$