Need someone good at math...

[Yosei]

Teach me how to reduce rational expressions to their lowest form 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

[Sparkeh]

:/

We never study this kinda things. Even in highschool.

Good luck.

[Destrus]

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.

[Hessah]

WOW... memories...

[Belaslav]

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)