Solve y^2+2y+1/5y-10*y^2-3y+2/y^2-1

$$\frac { y ^ { 2 } + 2 y + 1 } { 5 y - 10 } \cdot \frac { y ^ { 2 } - 3 y + 2 } { y ^ { 2 } - 1 }$$

Evaluate

$$\frac{y+1}{5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-3y+2}{y^{2}-1}.

$$\frac{y^{2}+2y+1}{5y-10}\times \frac{\left(y-2\right)\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{y^{2}+2y+1}{5y-10}\times \frac{y-2}{y+1}$$

Multiply \frac{y^{2}+2y+1}{5y-10} times \frac{y-2}{y+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}+2y+1\right)\left(y-2\right)}{\left(5y-10\right)\left(y+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(y-2\right)\left(y+1\right) in both numerator and denominator.

$$\frac{y+1}{5}$$

Expand

$$\frac{y+1}{5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-3y+2}{y^{2}-1}.

$$\frac{y^{2}+2y+1}{5y-10}\times \frac{\left(y-2\right)\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{y^{2}+2y+1}{5y-10}\times \frac{y-2}{y+1}$$

Multiply \frac{y^{2}+2y+1}{5y-10} times \frac{y-2}{y+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}+2y+1\right)\left(y-2\right)}{\left(5y-10\right)\left(y+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(y-2\right)\left(y+1\right) in both numerator and denominator.

$$\frac{y+1}{5}$$