please explain... ( q^2 - p^2 ) / (q - p) = q + p

Question

please explain how  ( q^2 - p^2 ) / (q - p) 
is rewritten to = q + p 

Answer 1

Factor the numerator as a difference of squares, and then it will be clear.

 

q² - p² = (q - p)(q + p)

 

If q - p ≠ 0,

 

(q² - p²) = [(q - p)(q + p)] / (q - p) = q + p