Solve y/y-1-y-1/y

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{yy}{y\left(y-1\right)} and \frac{\left(y-1\right)\left(y-1\right)}{y\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in yy-\left(y-1\right)\left(y-1\right).

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

Combine like terms in y^{2}-y^{2}+y+y-1.

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

Expand y\left(y-1\right).

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

Expand

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

Short Solution Steps

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

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

Since \frac{yy}{y\left(y-1\right)} and \frac{\left(y-1\right)\left(y-1\right)}{y\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in yy-\left(y-1\right)\left(y-1\right).

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

Combine like terms in y^{2}-y^{2}+y+y-1.

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

Expand y\left(y-1\right).

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