Question

What do I fill in the boxes?

Answer 1

see explanation

Explanation:

Given

`(4x+1)/(x^2-4x-12)` ← factorise the denominator

x² - 4x - 12 = (x - 6)(x + 2)

The fraction can now be expressed as

=
`(4x+1)/((x-6)(x+2))`

Split the numerator into its 2 parts, that is

=
`(4x)/((x-6)(x+2))` +
`(1)/((x-6)(x+2))`