Hello everybody!
I hope you feel for some algebra!
Problem 1 (I have "solved" this one, "solution" below)
Spoiler! - UPDATED
This is how I think
First we put as a fraction
Then we multiply with to get a common denominator.
Ok, now we are close to a more simpler way to put this problem. (Put everything in the same fraction.
is zero. we are left with
End Spoiler
A second opinion on this problem and it's "solution" is always welcome.
Alright, problem 2. Now we got to have a clear mind and a sharp eye to solve this one...
Solved!
First we work some on the first fraction, to make it more easy to work with. (I'll go more into detail later)
Problem 3
Solved!
Yes problem 2... I also try for a cd (common denominator). I suppose this would be something like a merged fraction:
Hmmm... the denominator seems fishy though, doesn't it?
Note: After a bit of thinking, I guess it is correct.
P.S.
Sorry for the double post, got carried away by all the math.
There are 3 fractions. Since the first two have the form (x+y),(x-z) with their denominators, combine them into one fraction only so the sqrt(ab) will be cleared in the denominator.
= [a(sqrt(ab) -b) +b(sqrt(ab) +a] /[(sqrt(ab) +a)(sqrt(ab) -b)]
= [a*sqrt(ab) -ab +b*sqrt(ab) +ab] /[ab -b*sqrt(ab) +a*sqrt(ab) -ab]
= [(a+b)sqrt(ab)] /[(a-b)sqrt(ab)]
= (a+b) /(a-b)
Now combine that to the 3rd fraction,
(a+b)/(a-b) -a/(a-b)
= (a+b -a)/(a-b)
= b/(a-b) -----------------answer.
I'm "quoting" the second part now. What is shown are "skeletons" of LaTex. How could I explain these now?
Anyway, step 1 is not 4 over all of those.
Rather, step 1 is, [4/(sqrt(5) -3)] +[3] +[sqrt(5)]
Or, [4/(sqrt(5) -3)] +[3/1] +[sqrt(5) /1]
The +3 +sqrt(5) are not under the 4.
See again my solution.
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Now, suppose your step 1 is correct, how did you arrive to your step 2?
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ticbol, do I understand you correctly? I disagree with you concerning step 1, 2.
No, you do not understand my solution.
Yes, you should disagree with yourself concerning your steps 1 and 2.
Haha do you prefer raw latex code? Please put it in formula, I can't follow your method by raw code.I'm "quoting" the second part now. What is shown are "skeletons" of LaTex. How could I explain these now?
Anyway, step 1 is not 4 over all of those.
Rather, step 1 is, [4/(sqrt(5) -3)] +[3] +[sqrt(5)]
Or, [4/(sqrt(5) -3)] +[3/1] +[sqrt(5) /1]
The +3 +sqrt(5) are not under the 4.
See again my solution.
I worked some more on it and here is what I have:Now, suppose your step 1 is correct, how did you arrive to your step 2?
Now we multiply each fraction with the two different denominators, we'll get a common denominator, , with this method.
Now we can easily put them together
Now some parts neutralizes each other, I'll skip the removal part because I can't picture it in Latex, (maybe if I knew how to use the horizontal line command).
The denominator is neutralized, and corresponding amount is removed from the numerator.
However, going from here gets wierd, we can remove different sets and thus get an different answer, can't we?
Example:
Let's open up the parentises
Note: I am not 100% sure of the following
Note: Oh my gosh! Wrong operator! Quick correction
@ Khrizalid
I have worked some on your method by dividing things up into square roots, but I am not coming anywhere with it.
Your answer to the first question is 0.
You have failed to multiply sqrt(5) - 3 properly in the second term.
The second term should read (sqrt(5) - 3)(3+sqrt(5)).
This results in 5 - 9 which is -4.
The first term is +4 so you get 0 over the common denominator of sqrt(5) - 3.
In the second problem, the denominator can be reduced to (a-b)^2(sqrt(ab))
In fairness, and please feel free to be embarassed about this by all means, I wasn't actually responding to you but to the original poster who had disputed your finding.
I could have probably made that clearer when I responded but we would have missed the fun of awkwardness .