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multiplying rational expressions...that don't factor

Started by fadilthrejk May 15, 2003 at 1:03 PM 1 replies 350+ views

Original Post

May 15, 2003 at 1:03 PM

I know that when you have two rational expressions and want to multiply them, you''re supposed to factor and eliminate common factors...yadda yadda yadda. But what if only either the numerator or denominator of each of them is factorable...that is, what if you can only factor half of each of the rational expressions? something like this: [(2x^2 + 5x - 3) / (x - 4)(x + 3)] * [((x - 2)(x + 1)) / (2x^2 - 5x + 2)] I have already factored the numerator of the second and the denominator of the first, so what would I do now...I don''t see how I can go any further? Is there some way I could pull something out of the unfactorable expressions? I am not asking for an answer to this, I just want to know how to do it. So don''t tell me the answer, please, as I want to learn and do the work myself. [edited by - fadilthrejk on March 19, 2002 at 4:53 AM]

Way Walker

May 15, 2003 at 2:16 PM

Forgive me if I''m wrong, but I think you just have to multiply it out a live with the fact that there are no common factors to cancel. Much like multiplying rational numbers without common factors.

(2/7)(3/5) = 6/35

There are no common terms, so there''s no canceling to be done. You could factor the top and bottom out and get

(2/7)(3/5) = 6/35 = (2*3)/(5*7)

Which may or may not be simplified for your purposes.

fadilthrejk

May 15, 2003 at 2:51 PM

I got it, you do this:

  
3x2 + 14x + 8
ac = 24 and b = 14
since both b and ac are positive, both factors will be positive
the factors of 24 are 1,24
                                2, 12
                                3, 8
                                 4,6
2 and 12 add to be 24
so we use 2 and 12 to break up the middle term
3x2 + 2x + 12x + 8; note: we have not changed the problem since 2x + 12x = 14x
Now we can use factoring by grouping
(3x2 + 2x) + (12x + 8)
x(3x + 2) + 4(3x + 2)
and our answer is (3x + 2)(x + 4)

It is an example from BigChalk.com. I didn''t know that was possible, but it is! I just figured out in 10 minutes what I have been dwelling upon for days.
Don''t you hate when that happens?

[edited by - fadilthrejk on March 19, 2002 at 4:53 AM]

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