Solve y-3/y+7=y-3/y+3

$$\frac { y - 3 } { y + 7 } = \frac { y - 3 } { y + 3 }$$

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -7,-3 since division by zero is not defined. Multiply both sides of the equation by \left(y+3\right)\left(y+7\right), the least common multiple of y+7,y+3.

$$\left(y+3\right)\left(y-3\right)=\left(y+7\right)\left(y-3\right)$$

Consider \left(y+3\right)\left(y-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$y^{2}-9=\left(y+7\right)\left(y-3\right)$$

Use the distributive property to multiply y+7 by y-3 and combine like terms.

$$y^{2}-9=y^{2}+4y-21$$

Subtract y^{2} from both sides.

$$y^{2}-9-y^{2}=4y-21$$

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

$$-9=4y-21$$

Swap sides so that all variable terms are on the left hand side.

$$4y-21=-9$$

Add 21 to both sides.

$$4y=-9+21$$

Add -9 and 21 to get 12.

$$4y=12$$

Divide both sides by 4.

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

Divide 12 by 4 to get 3.

$$y=3$$