How do you simplify (3x)/(x^2-x-6) + (x+2) / (x^2-6x+9)?

$\frac{4 {x}^{2} - 5 x + 4}{{x}^{3} - 4 {x}^{2} - 3 x + 18}$

Explanation:

Let's combine the fractions by first factoring the denominators:

$\frac{3 x}{{x}^{2} - x - 6} + \frac{x + 2}{{x}^{2} - 6 x + 9}$

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

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

$\frac{3 {x}^{2} - 9 x}{\left(x - 3\right) \left(x - 3\right) \left(x + 2\right)} + \frac{{x}^{2} + 4 x + 4}{\left(x - 3\right) \left(x - 3\right) \left(x + 2\right)}$

$\frac{4 {x}^{2} - 5 x + 4}{\left(x - 3\right) \left(x - 3\right) \left(x + 2\right)} = \frac{4 {x}^{2} - 5 x + 4}{{x}^{3} - 4 {x}^{2} - 3 x + 18}$