Solve 3/n-2-6n/n-6

$$\frac { 3 } { n - 2 } - \frac { 6 n } { n - 6 }$$

Evaluate

$$\frac{3\left(-2n^{2}+5n-6\right)}{\left(n-6\right)\left(n-2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n-2 and n-6 is \left(n-6\right)\left(n-2\right). Multiply \frac{3}{n-2} times \frac{n-6}{n-6}. Multiply \frac{6n}{n-6} times \frac{n-2}{n-2}.

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

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

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

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

$$\frac{3n-18-6n^{2}+12n}{\left(n-6\right)\left(n-2\right)}$$

Combine like terms in 3n-18-6n^{2}+12n.

$$\frac{15n-18-6n^{2}}{\left(n-6\right)\left(n-2\right)}$$

Expand \left(n-6\right)\left(n-2\right).

$$\frac{15n-18-6n^{2}}{n^{2}-8n+12}$$

Factor

$$\frac{3\left(-2n^{2}+5n-6\right)}{\left(n-6\right)\left(n-2\right)}$$