Why is the L.C.D (P + 2)(P - 2)?

Question

(p/p - 2) - (p²/p² - 4)

Answer 1

p/(p-2) - p²/(p²-4)

 

p² - 4 is a difference of squares, which has the general form a² - b² which factors to (a+b)(a-b). p²-4 is p² - 2² so it factors to (p+2)(p-2).  To verify, FOIL it out and you'll get p² - 4.  Hence:

 

p/(p-2) - p²/(p²-4) = p/(p-2) - p²/((p+2)(p-2))

 

The LCD is of (p-2) and (p+2)(p-2) is (p+2)(p-2).