Solve -1/left(2-yright)^2-1/y^2

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2-y\right)^{2} and y^{2} is y^{2}\left(-y+2\right)^{2}. Multiply \frac{-1}{\left(2-y\right)^{2}} times \frac{y^{2}}{y^{2}}. Multiply \frac{1}{y^{2}} times \frac{\left(-y+2\right)^{2}}{\left(-y+2\right)^{2}}.

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

Since \frac{-y^{2}}{y^{2}\left(-y+2\right)^{2}} and \frac{\left(-y+2\right)^{2}}{y^{2}\left(-y+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -y^{2}-\left(-y+2\right)^{2}.

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

Combine like terms in -y^{2}-y^{2}+4y-4.

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

Expand y^{2}\left(-y+2\right)^{2}.

$$\frac{-2y^{2}+4y-4}{y^{4}-4y^{3}+4y^{2}}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2-y\right)^{2} and y^{2} is y^{2}\left(-y+2\right)^{2}. Multiply \frac{-1}{\left(2-y\right)^{2}} times \frac{y^{2}}{y^{2}}. Multiply \frac{1}{y^{2}} times \frac{\left(-y+2\right)^{2}}{\left(-y+2\right)^{2}}.

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

Since \frac{-y^{2}}{y^{2}\left(-y+2\right)^{2}} and \frac{\left(-y+2\right)^{2}}{y^{2}\left(-y+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -y^{2}-\left(-y+2\right)^{2}.

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

Combine like terms in -y^{2}-y^{2}+4y-4.

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

Expand y^{2}\left(-y+2\right)^{2}.

$$\frac{-2y^{2}+4y-4}{y^{4}-4y^{3}+4y^{2}}$$