Solve 4/x-1+2/x+2

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

Evaluate

$$\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x+2 is \left(x-1\right)\left(x+2\right). Multiply \frac{4}{x-1} times \frac{x+2}{x+2}. Multiply \frac{2}{x+2} times \frac{x-1}{x-1}.

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

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

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

Do the multiplications in 4\left(x+2\right)+2\left(x-1\right).

$$\frac{4x+8+2x-2}{\left(x-1\right)\left(x+2\right)}$$

Combine like terms in 4x+8+2x-2.

$$\frac{6x+6}{\left(x-1\right)\left(x+2\right)}$$

Expand \left(x-1\right)\left(x+2\right).

$$\frac{6x+6}{x^{2}+x-2}$$

Factor

$$\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+2\right)}$$