Question

Find the least common denominator of 2x+8, 4x - 24

Answer 1

`LCD= 4 (x+4)(x-6)` or

`LCD= 4x^2 -8x-96`

Explanation:

Given

2x + 8 and 4x - 24

Required

Determine the least common denominator (LCD)

To calculate the LCD, we need to first get the factor of both expression

`2x + 8 = 2 * (x + 4)`

`4x - 24 = 2 * 2 * (x -6)`

Next, we list out and multiply the union of the factors; i.e. the combination of all term in each factor

This gives the LCD

`LCD= 2 * 2 * (x+4) * (x-6)`

`LCD = 4 * (x+4)(x-6)`

`LCD= 4 (x+4)(x-6)`

The answer can be left in this form of solved further:

`LCD= (4x+16)(x-6)`

`LCD= 4x^2 -24x + 16x-96`

`LCD= 4x^2 -8x-96`