Solve y-2/y+2=y-1/y+7

$$\frac{ y-2 }{ y+2 } = \frac{ y-1 }{ y+7 }$$

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -7,-2 since division by zero is not defined. Multiply both sides of the equation by \left(y+2\right)\left(y+7\right), the least common multiple of y+2,y+7.

$$\left(y+7\right)\left(y-2\right)=\left(y+2\right)\left(y-1\right)$$

Use the distributive property to multiply y+7 by y-2 and combine like terms.

$$y^{2}+5y-14=\left(y+2\right)\left(y-1\right)$$

Use the distributive property to multiply y+2 by y-1 and combine like terms.

$$y^{2}+5y-14=y^{2}+y-2$$

Subtract y^{2} from both sides.

$$y^{2}+5y-14-y^{2}=y-2$$

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

$$5y-14=y-2$$

Subtract y from both sides.

$$5y-14-y=-2$$

Combine 5y and -y to get 4y.

$$4y-14=-2$$

Add 14 to both sides.

$$4y=-2+14$$

Add -2 and 14 to get 12.

$$4y=12$$

Divide both sides by 4.

$$y=\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$y=3$$