Solve y^2-4y+4/y^2-2ydivy^2-4/y-2

$$\frac { y ^ { 2 } - 4 y + 4 } { y ^ { 2 } - 2 y } \div \frac { y ^ { 2 } - 4 } { y - 2 }$$

Evaluate

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

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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