Solve y-8/y-4=y+1/y+3

$$\frac { y - 8 } { y - 4 } = \frac { y + 1 } { y + 3 }$$

Solve for y

$$y=-10$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -3,4 since division by zero is not defined. Multiply both sides of the equation by \left(y-4\right)\left(y+3\right), the least common multiple of y-4,y+3.

$$\left(y+3\right)\left(y-8\right)=\left(y-4\right)\left(y+1\right)$$

Use the distributive property to multiply y+3 by y-8 and combine like terms.

$$y^{2}-5y-24=\left(y-4\right)\left(y+1\right)$$

Use the distributive property to multiply y-4 by y+1 and combine like terms.

$$y^{2}-5y-24=y^{2}-3y-4$$

Subtract y^{2} from both sides.

$$y^{2}-5y-24-y^{2}=-3y-4$$

Combine y^{2} and -y^{2} to get 0.

$$-5y-24=-3y-4$$

Add 3y to both sides.

$$-5y-24+3y=-4$$

Combine -5y and 3y to get -2y.

$$-2y-24=-4$$

Add 24 to both sides.

$$-2y=-4+24$$

Add -4 and 24 to get 20.

$$-2y=20$$

Divide both sides by -2.

$$y=\frac{20}{-2}$$

Divide 20 by -2 to get -10.

$$y=-10$$