Express $$\frac{4x}{x^2 - 9} - \frac{2}{x + 3}$$ as a single fraction in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 4

Now simplify the numerator:

$4x - 2(x - 3) = 4x - 2x + 6 = 2x + 6$

Thus, we can rewrite the expression as:

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

The numerator can be factored further:

$2(x + 3)$

Substituting this back:

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

Now, cancel the common factor of $(x + 3)$:

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

This is the final answer in its simplest form.