Solve 11/2y-22-y/11-y

$$\frac { 11 } { 2 y - 22 } - \frac { y } { 11 - y }$$

Evaluate

$$\frac{2y+11}{2\left(y-11\right)}$$

Short Solution Steps

Factor 2y-22.

$$\frac{11}{2\left(y-11\right)}-\frac{y}{11-y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(y-11\right) and 11-y is 2\left(y-11\right). Multiply \frac{y}{11-y} times \frac{-2}{-2}.

$$\frac{11}{2\left(y-11\right)}-\frac{-2y}{2\left(y-11\right)}$$

Since \frac{11}{2\left(y-11\right)} and \frac{-2y}{2\left(y-11\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-\left(-2y\right)}{2\left(y-11\right)}$$

Do the multiplications in 11-\left(-2y\right).

$$\frac{11+2y}{2\left(y-11\right)}$$

Expand 2\left(y-11\right).

$$\frac{11+2y}{2y-22}$$

Factor

$$\frac{2y+11}{2\left(y-11\right)}$$