Solve y+4/y-1-y-2/1-y

$$\frac { y + 4 } { y - 1 } - \frac { y - 2 } { 1 - y }$$

Evaluate

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

Short Solution Steps

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

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

Since \frac{y+4}{y-1} and \frac{-\left(y-2\right)}{y-1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in y+4-\left(-\left(y-2\right)\right).

$$\frac{y+4+y-2}{y-1}$$

Combine like terms in y+4+y-2.

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

Expand

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

Short Solution Steps

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

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

Since \frac{y+4}{y-1} and \frac{-\left(y-2\right)}{y-1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in y+4-\left(-\left(y-2\right)\right).

$$\frac{y+4+y-2}{y-1}$$

Combine like terms in y+4+y-2.

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