Solve y+2/y-3*y^2-6y+9/y^2-4

$$\frac { y + 2 } { y - 3 } \cdot \frac { y ^ { 2 } - 6 y + 9 } { y ^ { 2 } - 4 }$$

Evaluate

$$\frac{y-3}{y-2}$$

Short Solution Steps

Multiply \frac{y+2}{y-3} times \frac{y^{2}-6y+9}{y^{2}-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+2\right)\left(y^{2}-6y+9\right)}{\left(y-3\right)\left(y^{2}-4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y+2\right)\left(y-3\right)^{2}}{\left(y-3\right)\left(y-2\right)\left(y+2\right)}$$

Cancel out \left(y-3\right)\left(y+2\right) in both numerator and denominator.

$$\frac{y-3}{y-2}$$

Expand

$$\frac{y-3}{y-2}$$

Short Solution Steps

Multiply \frac{y+2}{y-3} times \frac{y^{2}-6y+9}{y^{2}-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+2\right)\left(y^{2}-6y+9\right)}{\left(y-3\right)\left(y^{2}-4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y+2\right)\left(y-3\right)^{2}}{\left(y-3\right)\left(y-2\right)\left(y+2\right)}$$

Cancel out \left(y-3\right)\left(y+2\right) in both numerator and denominator.

$$\frac{y-3}{y-2}$$