Solve y-1-8/y+1/frac{y^2-6y+9{y^2+y}}

$$\frac{ y-1- \frac{ 8 }{ y+1 } }{ \frac{ { y }^{ 2 } -6y+9 }{ { y }^{ 2 } +y } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y-1 times \frac{y+1}{y+1}.

$$\frac{\frac{\left(y-1\right)\left(y+1\right)}{y+1}-\frac{8}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Since \frac{\left(y-1\right)\left(y+1\right)}{y+1} and \frac{8}{y+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(y-1\right)\left(y+1\right)-8}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Do the multiplications in \left(y-1\right)\left(y+1\right)-8.

$$\frac{\frac{y^{2}+y-y-1-8}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Combine like terms in y^{2}+y-y-1-8.

$$\frac{\frac{y^{2}-9}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Divide \frac{y^{2}-9}{y+1} by \frac{y^{2}-6y+9}{y^{2}+y} by multiplying \frac{y^{2}-9}{y+1} by the reciprocal of \frac{y^{2}-6y+9}{y^{2}+y}.

$$\frac{\left(y^{2}-9\right)\left(y^{2}+y\right)}{\left(y+1\right)\left(y^{2}-6y+9\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(y-3\right)\left(y+1\right) in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y-1 times \frac{y+1}{y+1}.

$$\frac{\frac{\left(y-1\right)\left(y+1\right)}{y+1}-\frac{8}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Since \frac{\left(y-1\right)\left(y+1\right)}{y+1} and \frac{8}{y+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(y-1\right)\left(y+1\right)-8}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Do the multiplications in \left(y-1\right)\left(y+1\right)-8.

$$\frac{\frac{y^{2}+y-y-1-8}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Combine like terms in y^{2}+y-y-1-8.

$$\frac{\frac{y^{2}-9}{y+1}}{\frac{y^{2}-6y+9}{y^{2}+y}}$$

Divide \frac{y^{2}-9}{y+1} by \frac{y^{2}-6y+9}{y^{2}+y} by multiplying \frac{y^{2}-9}{y+1} by the reciprocal of \frac{y^{2}-6y+9}{y^{2}+y}.

$$\frac{\left(y^{2}-9\right)\left(y^{2}+y\right)}{\left(y+1\right)\left(y^{2}-6y+9\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(y-3\right)\left(y+1\right) in both numerator and denominator.

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

Expand the expression.

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