Answer:
[tex]x^3-7x^2-14x+120[/tex]
Step-by-step explanation:
The given rational expressions are [tex]\frac{5}{x^2-2x-24}[/tex] and [tex]\frac{-2}{x^2-11x-30}[/tex]
The denominators are:
[tex]x^2-2x-24=(x-6)(x+4)[/tex]
and
[tex]x^2-11x+30=(x-6)(x-5)[/tex]
The least common factor of the denominators is [tex](x-6)(x+4)(x-5)[/tex]
We expand in we get:
[tex]x^3-7x^2-14x+120[/tex]
Therefore the LCD of the given rational expression is:[tex]x^3-7x^2-14x+120[/tex]
