Why is the result of my equation wrong?

Question

The equation I am talking about is:

 

 

p²−pq

-------

q²−p²

 

 

My result was:   p

                     ———

                       p+q

 

But, instead, it should be:   -p

                                       ———

                                        p+q

 

Where is my mistake?

 

 

 

 

Answer 1

Factor both the numerator and denominator. Note the denominator is a difference of squares.

 

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

 

= -p / (q + p)

 

 

Answer 2

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

Do you see your mistake now>

The factors you want to cancel from the numerator and denominator have opposite signs!

 

BTW you can only do that cancellation if p ≠ q,