Solve y^2-4y+4/5y+10*y^2-y-6/y^2-5y+6

$$\frac { y ^ { 2 } - 4 y + 4 } { 5 y + 10 } \cdot \frac { y ^ { 2 } - y - 6 } { y ^ { 2 } - 5 y + 6 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-y-6}{y^{2}-5y+6}.

$$\frac{y^{2}-4y+4}{5y+10}\times \frac{\left(y-3\right)\left(y+2\right)}{\left(y-3\right)\left(y-2\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{y^{2}-4y+4}{5y+10}\times \frac{y+2}{y-2}$$

Multiply \frac{y^{2}-4y+4}{5y+10} times \frac{y+2}{y-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-4y+4\right)\left(y+2\right)}{\left(5y+10\right)\left(y-2\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-y-6}{y^{2}-5y+6}.

$$\frac{y^{2}-4y+4}{5y+10}\times \frac{\left(y-3\right)\left(y+2\right)}{\left(y-3\right)\left(y-2\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{y^{2}-4y+4}{5y+10}\times \frac{y+2}{y-2}$$

Multiply \frac{y^{2}-4y+4}{5y+10} times \frac{y+2}{y-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-4y+4\right)\left(y+2\right)}{\left(5y+10\right)\left(y-2\right)}$$

Factor the expressions that are not already factored.

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

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

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