help me please

Let's take an example

5 / (x - 1)    +  3 / (x + 2 )   =  5

The LCM  is  (x - 1) ( x + 2)

So

5 (x - 1) ( x + 2) / (x - 1)  + 3(x - 1) ( x + 2) / (x + 2)   =  5(x - 1) ( x + 2)

5(x + 2)  + 3(x - 1)  = 5(x - 1) ( x + 2)

So...multiplying by the LCM    "cancels out" the denominators

presumably because the LCD would be factors of everything on both sides, meaning all the denominators are "canceled"?