Solve 3/n+2-3/n+3=

$$\frac { 3 } { n + 2 } - \frac { 3 } { n + 3 } =$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

$$\frac{3n+9-3n-6}{\left(n+2\right)\left(n+3\right)}$$

Combine like terms in 3n+9-3n-6.

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

Expand \left(n+2\right)\left(n+3\right).

$$\frac{3}{n^{2}+5n+6}$$

Factor

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