Solve y^2-2y-15/y^2-9div12-4y/y^2-6y+9

$$\frac{ { y }^{ 2 } -2y-15 }{ { y }^{ 2 } -9 } \div \frac { 12-4y } { { y }^{ 2 } -6y+9 }$$

Evaluate

$$\frac{5-y}{4}$$

Short Solution Steps

Divide \frac{y^{2}-2y-15}{y^{2}-9} by \frac{12-4y}{y^{2}-6y+9} by multiplying \frac{y^{2}-2y-15}{y^{2}-9} by the reciprocal of \frac{12-4y}{y^{2}-6y+9}.

$$\frac{\left(y^{2}-2y-15\right)\left(y^{2}-6y+9\right)}{\left(y^{2}-9\right)\left(12-4y\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-5\right)\left(y+3\right)\left(y-3\right)^{2}}{4\left(y-3\right)\left(y+3\right)\left(-y+3\right)}$$

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

$$\frac{\left(y-5\right)\left(y-3\right)}{4\left(-y+3\right)}$$

Extract the negative sign in -3+y.

$$\frac{-\left(y-5\right)\left(-y+3\right)}{4\left(-y+3\right)}$$

Cancel out -y+3 in both numerator and denominator.

$$\frac{-\left(y-5\right)}{4}$$

Expand the expression.

$$\frac{-y+5}{4}$$

Expand

$$\frac{5-y}{4}$$

Short Solution Steps

Divide \frac{y^{2}-2y-15}{y^{2}-9} by \frac{12-4y}{y^{2}-6y+9} by multiplying \frac{y^{2}-2y-15}{y^{2}-9} by the reciprocal of \frac{12-4y}{y^{2}-6y+9}.

$$\frac{\left(y^{2}-2y-15\right)\left(y^{2}-6y+9\right)}{\left(y^{2}-9\right)\left(12-4y\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-5\right)\left(y+3\right)\left(y-3\right)^{2}}{4\left(y-3\right)\left(y+3\right)\left(-y+3\right)}$$

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

$$\frac{\left(y-5\right)\left(y-3\right)}{4\left(-y+3\right)}$$

Extract the negative sign in -3+y.

$$\frac{-\left(y-5\right)\left(-y+3\right)}{4\left(-y+3\right)}$$

Cancel out -y+3 in both numerator and denominator.

$$\frac{-\left(y-5\right)}{4}$$

Expand the expression.

$$\frac{-y+5}{4}$$