Solve 2/y-2+3/y+6=0

$$\frac{ 2 }{ y-2 } + \frac{ 3 }{ y+6 } = 0$$

Solve for y

$$y = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

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

$$\left(y+6\right)\times 2+\left(y-2\right)\times 3=0$$

Use the distributive property to multiply y+6 by 2.

$$2y+12+\left(y-2\right)\times 3=0$$

Use the distributive property to multiply y-2 by 3.

$$2y+12+3y-6=0$$

Combine 2y and 3y to get 5y.

$$5y+12-6=0$$

Subtract 6 from 12 to get 6.

$$5y+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$5y=-6$$

Divide both sides by 5.

$$y=\frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$y=-\frac{6}{5}$$