Algebra
posted by Sara .
Posted by Tammy on Thursday, July 19, 2007 at 10:12pm.
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(3x+4)/(3x4)+(3x4)/(3x+4)
 Divide top by bottom
(3x4)/(3x+4)(3x+4)/(3x4)
Very Big Problem and help would be greatly appreciated
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Algebra  Reiny, Thursday, July 19, 2007 at 11:59pm
not that tough once you notice that your question has the pattern
(a/b + b/a)÷(b/a  a/b)
where a = 3x+4 and b=3x4
this easily reduces to (a^2 + b^2)/(b^2  a^2)
now replace a and b with 3x+4 and 3x4 and it simplifies to
(9x^2+16)/(24x)
hmm, the answer is right (it's in my book) but I don't understand how you simply reduce it to (a^2+b^2) (b^2a^2)
and from there when I tried to replace a and b with 3x+4 and 3x4 I don't know how to simplify it or get the answer. Could you write down the steps detailed? I have a bunch of problems that I can't solve that are similar, so I think if I understand the concept of this one I will be able to sove all the other ones.
The fact that there was that nice symmetry to the question, makes it easier than it first appears.
I had it as:
(a/b + b/a)÷(b/a  a/b)
look at (a/b + b/a)
the common denominator for this would be ab, so
a/b + b/a = (a^2 + b^2)/ab
similarly for
(b/a  a/b) the common denominator is ab and this reduces to
(b^2  a^2)/ab
so now we have
(a^2 + b^2)/ab ÷ (b^2  a^2)/ab
remember when dividing one fraction by another, we multiply by the reciprocal of the second fraction, so
(a^2 + b^2)/ab ÷ (b^2  a^2)/ab
=(a^2 + b^2)/ab * ab/((b^2  a^2)
the ab's cancel and that's how I got
(a^2 + b^2)/(b^2  a^2)
Now replace the original values of a and b and you should be able to do that yourself.
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