Solve 7/y^2-4-4/y+2=5/y-2

$$\frac { 7 } { y ^ { 2 } - 4 } - \frac { 4 } { y + 2 } = \frac { 5 } { y - 2 }$$

Solve for y

$$y=\frac{5}{9}\approx 0.555555556$$

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}-4,y+2,y-2.

$$7-\left(y-2\right)\times 4=\left(y+2\right)\times 5$$

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

$$7-\left(4y-8\right)=\left(y+2\right)\times 5$$

To find the opposite of 4y-8, find the opposite of each term.

$$7-4y+8=\left(y+2\right)\times 5$$

Add 7 and 8 to get 15.

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

Use the distributive property to multiply y+2 by 5.

$$15-4y=5y+10$$

Subtract 5y from both sides.

$$15-4y-5y=10$$

Combine -4y and -5y to get -9y.

$$15-9y=10$$

Subtract 15 from both sides.

$$-9y=10-15$$

Subtract 15 from 10 to get -5.

$$-9y=-5$$

Divide both sides by -9.

$$y=\frac{-5}{-9}$$

Fraction \frac{-5}{-9} can be simplified to \frac{5}{9} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{5}{9}$$