Solve y^2-4y+3/y^2+y-2*y^2-2y-15/y^2-9

$$\frac { y ^ { 2 } - 4 y + 3 } { y ^ { 2 } + y - 2 } \times \frac { y ^ { 2 } - 2 y - 15 } { y ^ { 2 } - 9 }$$

Evaluate

$$\frac{y-5}{y+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-4y+3}{y^{2}+y-2}.

$$\frac{\left(y-3\right)\left(y-1\right)}{\left(y-1\right)\left(y+2\right)}\times \frac{y^{2}-2y-15}{y^{2}-9}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{y-3}{y+2}\times \frac{y^{2}-2y-15}{y^{2}-9}$$

Factor the expressions that are not already factored in \frac{y^{2}-2y-15}{y^{2}-9}.

$$\frac{y-3}{y+2}\times \frac{\left(y-5\right)\left(y+3\right)}{\left(y-3\right)\left(y+3\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y-3}{y+2}\times \frac{y-5}{y-3}$$

Multiply \frac{y-3}{y+2} times \frac{y-5}{y-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-3\right)\left(y-5\right)}{\left(y+2\right)\left(y-3\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{y-5}{y+2}$$

Expand

$$\frac{y-5}{y+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-4y+3}{y^{2}+y-2}.

$$\frac{\left(y-3\right)\left(y-1\right)}{\left(y-1\right)\left(y+2\right)}\times \frac{y^{2}-2y-15}{y^{2}-9}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{y-3}{y+2}\times \frac{y^{2}-2y-15}{y^{2}-9}$$

Factor the expressions that are not already factored in \frac{y^{2}-2y-15}{y^{2}-9}.

$$\frac{y-3}{y+2}\times \frac{\left(y-5\right)\left(y+3\right)}{\left(y-3\right)\left(y+3\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y-3}{y+2}\times \frac{y-5}{y-3}$$

Multiply \frac{y-3}{y+2} times \frac{y-5}{y-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-3\right)\left(y-5\right)}{\left(y+2\right)\left(y-3\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{y-5}{y+2}$$