Solve y^2-10y+9/y^2-1*y+4/y^2-5y-36

$$\frac { y ^ { 2 } - 10 y + 9 } { y ^ { 2 } - 1 } \cdot \frac { y + 4 } { y ^ { 2 } - 5 y - 36 }$$

Evaluate

$$\frac{1}{y+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-10y+9}{y^{2}-1}.

$$\frac{\left(y-9\right)\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}\times \frac{y+4}{y^{2}-5y-36}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{y-9}{y+1}\times \frac{y+4}{y^{2}-5y-36}$$

Factor the expressions that are not already factored in \frac{y+4}{y^{2}-5y-36}.

$$\frac{y-9}{y+1}\times \frac{y+4}{\left(y-9\right)\left(y+4\right)}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{y-9}{y+1}\times \frac{1}{y-9}$$

Multiply \frac{y-9}{y+1} times \frac{1}{y-9} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out y-9 in both numerator and denominator.

$$\frac{1}{y+1}$$

Expand

$$\frac{1}{y+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-10y+9}{y^{2}-1}.

$$\frac{\left(y-9\right)\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}\times \frac{y+4}{y^{2}-5y-36}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{y-9}{y+1}\times \frac{y+4}{y^{2}-5y-36}$$

Factor the expressions that are not already factored in \frac{y+4}{y^{2}-5y-36}.

$$\frac{y-9}{y+1}\times \frac{y+4}{\left(y-9\right)\left(y+4\right)}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{y-9}{y+1}\times \frac{1}{y-9}$$

Multiply \frac{y-9}{y+1} times \frac{1}{y-9} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out y-9 in both numerator and denominator.

$$\frac{1}{y+1}$$