Answer:
[tex]LCD= 4 (x+4)(x-6)[/tex] or
[tex]LCD= 4x^2 -8x-96[/tex]
Step-by-step 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
[tex]2x + 8 = 2 * (x + 4)[/tex]
[tex]4x - 24 = 2 * 2 * (x -6)[/tex]
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
[tex]LCD= 2 * 2 * (x+4) * (x-6)[/tex]
[tex]LCD = 4 * (x+4)(x-6)[/tex]
[tex]LCD= 4 (x+4)(x-6)[/tex]
The answer can be left in this form of solved further:
[tex]LCD= (4x+16)(x-6)[/tex]
[tex]LCD= 4x^2 -24x + 16x-96[/tex]
[tex]LCD= 4x^2 -8x-96[/tex]
