Solve 1/2-y+1/y

$$\frac{ 1 }{ 2-y } + \frac{ 1 }{ y }$$

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in y-y+2.

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

Expand y\left(-y+2\right).

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

Differentiate w.r.t. y

$$\frac{4\left(1-y\right)}{\left(2-y\right)\left(y-2\right)y^{2}}$$