PLAESE HELP!!! complex fractions!

[snickers]

w/w^2 + w+3w/w^4-1 - 1/w-1

so i thought i would have to to do difference of 2 perfect squares for that middle part at first and have (after all factoring of it) ... (x^2+1)(x-1)(x+1).. and that would be my LCD for all 3 fractions. When i then tried to combine all three numerators for that denominator, i came up with, 2w^2+4w-w^3-w^2-w-1 which can then be simplified to w^2+3w-w^3-1...all the while this is still over the denominator of (x^2+1)(w-1)(w+1). but i do not know what to do from there on. can someone please tell me what i may have done wrong in my steps or if i have made it that far right, and just help me with the next step. by the way, the answer at the very end is supposed to be... 1/(w+1)(w^2+1)

 

[arthur ohlsten]

1
let us assume the answer is ____________ then for w=2
(w+1)(w^2+1)

1 1
_________ = ______
3*5 15



But if I substitute w=2 into your original fraction I don't get 1/15

Are you sure the fraction is correct? The answer appears to be the type you would expect a students answer to look like.

Arthur

 

[soroban]

Hello, snickers!

w/w^2 + w+3w/w^4-1 - 1/w-1

Some parentheses would help . . .

I assume the problem is: \(\displaystyle \L\,\frac{w}{w^2}\,+\,\frac{w\,+\,3w}{w^4\,-\,1}\,-\,\frac{1}{w\,-\1}\)

\(\displaystyle \;\;\)but I get nothing like their answer!


A strangely constructed problem . . .
\(\displaystyle \;\;\)the first fraction can be reduced . . . the second can be simplied!

\(\displaystyle \;\;\)then we have: \(\displaystyle \L\,\frac{1}{w}\,+\,\frac{4w}{w^4\,-\,1}\,-\,\frac{1}{w\,-\,1}\;\;\)[Did they do that just to annoy us?]


The LCD is: \(\displaystyle \,w(w\,-\,1)(w\,+\,1)(w^2\,+\,1)\)

The fractions become: \(\displaystyle \L\:\frac{(w-1)(w+1)(w^2+1)}{w(w-1)(w+1)(w^1+1)}\,+\,\frac{4w(w)}{w(w-1)(w+1)(w^2+1)}\,-\,\frac{w(w+1)(w^2+1)}{w(w-1)(w+1)(w^2+1)}\)

\(\displaystyle \L\;\;=\;\frac{w^4\,-\,1\,+\,4w^2\,-(w^4\,+\,w^3\,+\,w^2\,+\,w)}{w(w\,-\,1)(w\,+\,1)(w^2\,+\,1)} \;=\;\frac{-w^3\,-\,3w^2\,-\,w\,-\,1}{w(w\,-\,1)(w\,+\,1)(w^2\,+\,1)}\)

So what's going on ??

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I believe there are typos in the original problem.
\(\displaystyle \;\;\)The first two fractions are rather suspect.

The problem was probably: \(\displaystyle \L\,\frac{w}{w^2\,\pm\,1}\,+\,\frac{w\,+\,3}{w^4\,-\,1}\,-\,\frac{1}{w\,-\,1}\)

But even these don't come out to the given answer.
\(\displaystyle \;\;\)And I'm flat out of ideas . . .

 

[snickers]

I'm positive the answer is right. my teacher gave us the answers to the homework before she gave it to us. and i double and triple checked, there isnt any typos in it. so i guess ill just tell me teacher that i couldnt figure it out. i got the same results as both of you, and i dont know what to do either. its really confusing. thanks for the help though