Question

Find the LCD of$\frac{5}{x^2-2x-8},\frac{2x}{x^2-x-12}$.

Short answer

The LCD is$x^3+x^2-14x-24$.

Step-by-step solution

Given Information

The given expression is$\frac{5}{x^2-2x-8},\frac{2x}{x^2-x-12}$.

Factor the denominator of both expressions

The factored form of first denominator.

$x^2-2x-8=(x-4)(x+2)$

The factored form of second denominator.

$x^2-x-12=(x-4)(x+3)$

 Determine the common factors and from the remaining factors, multiply each of the denominator with appropriate factors.

The common factor is $(x-4)$.

Multiply common factor with other factors.

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

$=x^3+x^2-14x-24$.