SOLUTION: Hi I need help on 2 question. I think you can solve them the same way... ((25-p^2)/12)x(6/(p-5)) I hope i made the problem clear enough thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I need help on 2 question. I think you can solve them the same way... ((25-p^2)/12)x(6/(p-5)) I hope i made the problem clear enough thank you      Log On


   

Question 229925: Hi I need help on 2 question. I think you can solve them the same way...
((25-p^2)/12)x(6/(p-5))
I hope i made the problem clear enough
thank you
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2825-p%5E2%29%2F12%29%286%2F%28p-5%29%29

Whenever you multiply fractions, it is a good idea to cancel common factors before actually multiplying. It makes the multiplying easier and the reducing of the fraction easier. In order to cancel common factors we have to have factors. So the first order of business is to factor all the numerators and denominators:
%28%28%285%2Bp%29%285-p%29%29%2F%282%2A2%2A3%29%29%28%282%2A3%29%2F%28p-5%29%29
The obvious factors that cancel are the 2's and 3's. But it is helpful to realize that (5-p) and (p-5) are negatives of each other. (Think about it.) So they will match if we factor out a -1 from one of them:
%28%28%285%2Bp%29%28-1%29%28p-5%29%29%2F%282%2A2%2A3%29%29%28%282%2A3%29%2F%28p-5%29%29
Now can cancel to maximum effect:

leaving:
%28%28%285%2Bp%29%28-1%29%29%2F2%29%281%2F1%29
Simplifying we get:
%28-5-p%29%2F2