Solve y+3/y-1=y+2/y-3

$$\frac { y + 3 } { y - 1 } = \frac { y + 2 } { y - 3 }$$

Solve for y

$$y=-7$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values 1,3 since division by zero is not defined. Multiply both sides of the equation by \left(y-3\right)\left(y-1\right), the least common multiple of y-1,y-3.

$$\left(y-3\right)\left(y+3\right)=\left(y-1\right)\left(y+2\right)$$

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.

$$y^{2}-9=\left(y-1\right)\left(y+2\right)$$

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

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

Subtract y^{2} from both sides.

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

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

$$-9=y-2$$

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

$$y-2=-9$$

Add 2 to both sides.

$$y=-9+2$$

Add -9 and 2 to get -7.

$$y=-7$$