Need help verifying an anwer to this problem.  TOPIC_SOLVED

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Need help verifying an anwer to this problem.

Postby rogermiranda on Sun May 23, 2010 7:35 pm

Complex Fraction:
a^2 / b^2 - 1 denominator 1/a + 1/b = a^2 - b^2 / b^2 denominator b+a / ab
= a^2 - b^2 / b^2 * ab / b+a = a(a-b) / b.
But my textbook has the answer a(a-b). So what happened to the denominator b?
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Postby stapel_eliz on Sun May 23, 2010 10:59 pm

Please reply showing the expression with grouping symbols. For instance, does "a^2 / b^2 - 1" mean "(a2/b2) - 1" or "a2/(b2 - 1)"?

Thank you! :wink:
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Re: Need help verifying an anwer to this problem.

Postby rogermiranda on Mon May 24, 2010 3:49 pm

Here is the Complex Fraction:
Numerator= (a^2 / b^2) - 1
Denominator = (1/a + b/a)

So, finding the LCD I have
Numerator= (a^2 - b^2 / b^2)
Denominator = (b + a / ab)

Next I multiply by the reciprocal
(a^2 - b^2 / b^2) * (ab / b + a)
[(a + b)(a - b) / b^2)] * (ab / b + a)

Simplifying, I am left with
(a - b / b) * a

So the answer I get is
Numerator= a(a - b)
Denominator = b but my textbook has the answer a(a - b). So what happened to the denominator b?
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Postby stapel_eliz on Mon May 24, 2010 4:10 pm

rogermiranda wrote:Here is the Complex Fraction:
Numerator= (a^2 / b^2) - 1
Denominator = (1/a + b/a)

I will assume the following:

. . . . .

I think you then went the route of working the numerator and denominator separately. But I don't understand what you did in the denominator, since you were given two fractions with the same denominator...? I think the next step should have been as follows:

. . . . .

Please reply with clarification or corrections. Thank you! :wink:
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Re: Need help verifying an anwer to this problem.

Postby rogermiranda on Mon May 24, 2010 5:00 pm

Yes you have written the problem correctly.
Except the denomitor of the complex fraction is 1 over a + 1 over b (1/a + 1/b). So the LCD is ab.
So the denominator of the complex fraction is now b + a over ab (b + a / ab).
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  TOPIC_SOLVED

Postby stapel_eliz on Mon May 24, 2010 6:45 pm

rogermiranda wrote:... the denomitor of the complex fraction is 1 over a + 1 over b (1/a + 1/b).

Ah; so the expression is as follows...?

. . . . .

Then the LCD's would give:

. . . . .

Reverse the one addition to get the standard order:

. . . . .

Then flip-n-multiply:

. . . . .

Factor the one numerator, cancel the common factors, and simplify to get the final answer.

My answer matches yours, by the way, not the book's. At a guess, the solution was typoed. :oops:
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