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

Feb 19, 2016

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

#### Explanation:

Note: To add fraction, we need common denominator
Remember:factor of the difference of square
$\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$

Here is how we can simplify $\frac{2 x + 3}{{x}^{2} - 9} + \frac{x}{x - 3}$

Step 1 : Factor the denominator

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

Step 2: Find the common denominator

(2x+3)/((x-3)(x+3)) + x/(x-3)color(red)(((x+3)/(x+3))

Step 3: Multiply

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

Step 4: Combined like terms

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

We can't factor the numerator, therefore the answer stay as it is.