Expert: Sherman D. - 2/9/2005

Question
1. what I meant by parallel was that it was on equal difficulty as my previous problem.can you show me how to do that problem.
2. Also,why don't you use the negative 1 from "x-1?" when dividing?What's the explanation why you only use the x?I love math and don't just like rules;I like the explanations and logic to it.
Thanks for your time.It is well-appreciated.
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Followup To
Question -
(x^3-1)/(x-1)
I know the answer is x^2 +x +1,however I don't understand how to get that.
One reason is:
when my teacher did this problem on the board, he told us to go like regular long-division and he said to do x into x^3     (ie. x^3/x). My question is what happened to using the -1?That's one of my many problems on this.
I know somewhere along the line I'm missing a point.
Can you please help me.Thanks


If you can't help with this problem, I'm sure  this parallel problem will help me:
(470+3)/(10+5)
Just don't add them together and divide because then its not parallel!Thanks.
Answer -
(x^3 - 1)/(x - 1)
((x^2 + x + 1)(x - 1))/(x - 1)

the (x - 1)s cancel out, leaving you with

x^2 + x + 1 as your answer.

Think of it like this

((x^2 + x + 1)(x - 1))/(x - 1)
(x^2 + x + 1) * ((x - 1)/(x - 1))
same as
(x^2 + x + 1) * 1
or
x^2 + x + 1

If you have anymore let me know and i will try and answer them.

I will try and use synthetic division, because its easier to type out

(x^3 - 1)/(x - 1)
becomes
(x^3 + 0x^2 + 0x - 1)/(x - 1)

1'|'1'0'0'|'-1
''|'''1'1'|''1
----------------
''|'1'1'1'|''0

which makes the remaining equation

x^2 + x + 1

-----------------------------------------------------------

(470 + 3)/(10 + 5)
(473)/(15)
31.533333 or 31 + (8/15)

as for the word Parallel, sorry don't know what you mean.

Answer
1.)
I kinda understand you, and yet i can't do it because i explain it, if i completely understood you. I know what you mean by parallel, like what if (470 + 3)/(10 + 5) were like (x^3 - 1)/(x - 1) but thats about all i get.

How about this, you just send me the math problems you are having trouble with, and i will try and help you, and if i think it needs explaining, i will see if i can help you with that. Majority of the problem i do, i don't explain why its done that way, i just mathematically show you.

Even if you had a (ax^3 + bx^2 + cx + d)/(ex + f), you only have a few choices, use long division, by dividing the numerator by the denominator, use synthetic division and use (-f/e), or try and factor the numerator and denominator if needed, and take out one set of each of what matches. If you had a problem like
((x - 1)(x + 2)(x - 3))/(x + 2), then the (x + 2)s would cancel out, leaving you with (x - 1)(x - 3), or x^2 - 4x + 3

If factoring can't be used, i first go to synthetic division, since its a lot easier to use, but when it comes to having a quadratic equation in the denomintor, you first have to see if you can factor it, then first divide the numerator by one of the factors, then whatever you get out of that, divide that value by the next factor.
-----------------------------------------------------------

2.)
When using long division, you have to use both the x and the -1, like this

      ___________
x - 1 /x^3 - 1

which becomes
   
       ___________________
(x - 1)/x^3 + 0x^2 + 0x - 1

I would do the rest, but its really hard to show the work correctly with the work becoming left aligned

when using synthetic division, you have to use whatever value makes x equal 0.

As for me, when i can, i just like factoring, then cancelling out the values that match, but only one set for each, for example, if you have ((x - 1)(x - 1))/(x - 1), only one set of (x - 1)s cancel out.

Sorry i couldn't be of much more help. All i can suggest is to send me the math, and i will try and do it step by step. If you want long division, i will have to use synethic division instead, because long division doesn't turn out right when i do it. For ex:

        
''''''''_______x^2_+__x_+_1__
(x - 1)/x^3 + 0x^2 + 0x - 1
'''''''-x^3 - 'x^2
''''''-----------------
'''''''''''''''x^2 + 0x
'''''''''''''- x^2 - 'x
'''''''''''''---------------
''''''''''''''''''''''x - 1
''''''''''''''''''''- x - 1
''''''''''''''''''''--------
''''''''''''''''''''''''''0

The '''' is to keep it from becoming completely left aligned.