Need someone good at math...
 

Teach me how to reduce rational expressions to their lowest form :cries: I missed class and I never learned this in High School. So I'm on a quest for people who can explain it to me.

example problems:

1.
5+1
------
25-1

2.
25-30+9
----------
25-9

3.
a^2-3a
---------
a^3-8a^2+15a

:/

We never study this kinda things. Even in highschool.

Good luck.

i'll give this try, see what i can remember.

although you can just do the addition and subtraction in some of these i think i see what they want you to do.


1.
5+1
------
25-1

first you factor. 25-1 is a difference of squares. so it becomes (5+1)(5-1)

5+1
-----------
(5+1)(5-1)


then you can cancel out like terms where there's one in the numerator and denominator. here that's only the 5+1 term so it becomes

1
---- =
5-1

1
----
4







2.
25-30+9
----------
25-9

this one has a trinomial (i think that's right) in the numerator so it's a little more difficult but it still has the difference of squares which is easier to figure out in the denominator. 25-9 = (5+3)(5-3) so this is now

25-30+9
-----------
(5+3)(5-3)

the good thing about that is you know one of those two terms in the denominator is a factor of the trinomial in the numerator. you can use that to help you figure it out. also (and i just noticed this as typing out the sentence that would've gone here) that trinomial is a binomial squared. and because the last part is positive (+9), while the middle term is negative you know that the binomial has subtraction so it factors into (5-3)^2

(5-3)^2
---------- =
(5+3)(5-3)


(5-3)(5-3)
------------
(5+3)(5-3)

and again cancel out like terms. here that's the 5-3.

(5-3)
------
(5+3)

2
-
8

1
-
4 again o_O






3.
a^2-3a
---------
a^3-8a^2+15a

this one's a bit different since the factoring isn't the same as the previous ones. since we see a is common in each term we factor that out first

a(a-3)
---------------
a(a^2-8a+15)

the a's outside of the parentheses cancel out now

a-3
-----------
a^2-8a+15

now we factor the denominator and again we have a clue, this time in the numerator. one of the factors will be a-3. we can also gather like before that both factors are binomials with subtraction and can get a-5 as the second factor so we have

a-3
----------
(a-3)(a-5)

cancel out the a-3 and get

1
----
a-5




ok, that should all be correct and let me know if there's anything you don't get or anything that seems wrong.

WOW... memories...

You're not the only one, heh.

Bear in mind Yosei that only squares with a MINUS sign can be factored in this manner.

Ie.

The Right way: (a^2 - b^2)=(a+b)*(a-b)

Not: (a^2 + b^2)=/=(a+b)*(a-b)