Solve 6/x^2+2x-3/x+3/x+2

$$\frac { 6 } { x ^ { 2 } + 2 x } - \frac { 3 } { x } + \frac { 3 } { x + 2 }$$

Evaluate

$$0$$

Short Solution Steps

Factor x^{2}+2x.

$$\frac{6}{x\left(x+2\right)}-\frac{3}{x}+\frac{3}{x+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x+2\right) and x is x\left(x+2\right). Multiply \frac{3}{x} times \frac{x+2}{x+2}.

$$\frac{6}{x\left(x+2\right)}-\frac{3\left(x+2\right)}{x\left(x+2\right)}+\frac{3}{x+2}$$

Since \frac{6}{x\left(x+2\right)} and \frac{3\left(x+2\right)}{x\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-3\left(x+2\right)}{x\left(x+2\right)}+\frac{3}{x+2}$$

Do the multiplications in 6-3\left(x+2\right).

$$\frac{6-3x-6}{x\left(x+2\right)}+\frac{3}{x+2}$$

Combine like terms in 6-3x-6.

$$\frac{-3x}{x\left(x+2\right)}+\frac{3}{x+2}$$

Cancel out x in both numerator and denominator.

$$\frac{-3}{x+2}+\frac{3}{x+2}$$

Since \frac{-3}{x+2} and \frac{3}{x+2} have the same denominator, add them by adding their numerators. Add -3 and 3 to get 0.

$$\frac{0}{x+2}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

$$0$$