Solve -5/y+2-2/y-3=5/y^2-y-6

$$\frac { - 5 } { y + 2 } - \frac { 2 } { y - 3 } = \frac { 5 } { y ^ { 2 } - y - 6 }$$

Solve for y

$$y=\frac{6}{7}\approx 0.857142857$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -2,3 since division by zero is not defined. Multiply both sides of the equation by \left(y-3\right)\left(y+2\right), the least common multiple of y+2,y-3,y^{2}-y-6.

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

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

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

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

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

To find the opposite of 2y+4, find the opposite of each term.

$$-5y+15-2y-4=5$$

Combine -5y and -2y to get -7y.

$$-7y+15-4=5$$

Subtract 4 from 15 to get 11.

$$-7y+11=5$$

Subtract 11 from both sides.

$$-7y=5-11$$

Subtract 11 from 5 to get -6.

$$-7y=-6$$

Divide both sides by -7.

$$y=\frac{-6}{-7}$$

Fraction \frac{-6}{-7} can be simplified to \frac{6}{7} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{6}{7}$$