Answer
The LCM method is to be used whenever there is a common factor between the denominators as it will easily yield a reduced form.
Work Step by Step
The LCM method is to be used whenever there is a common factor between the denominators as it will easily yield a reduced form.
Examples:
a)
Consider the example where LCM is used.
$\dfrac{x-2}{(x-1)(x+2)}+\dfrac{3}{(x-1)^2}$
$=\dfrac{(x-2)(x-1)+3(x+2)}{(x-1)^2(x+2)}$
$=\dfrac{x^2-2x-x+2+3x+6}{(x-1)^2(x+2)}$
$=\dfrac{x^2+8}{(x-1)^2(x+2)}$
b)
Consider the example where LCM is not needed.
$\dfrac{x}{x-1}+\dfrac{2}{x-1}$
$=\dfrac{x+2}{x-1}$
Note that the denominators are already same.
