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October 29th, 2009, 04:56 AM   #1
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Simplifying Complex Fractions

How do you simplify this complex fraction?
1/a + 1/b over ab?

The answer given is b + a over a^2 times b^2 but I don't know how this was derived and I would like to see a step by step explanation if anyone could be so kind.

Thanks and cheers.
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October 29th, 2009, 05:25 AM   #2
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Re: Simplifying Complex Fractions

If you are wanting to simplify this fraction: , here's how:
These two are the same:
Combine the numerator into one fraction, using the least common multiple:

Now substitute this in for the numerator:

To divide by a fraction, you invert and multiply, so
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October 29th, 2009, 05:41 AM   #3
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Re: Simplifying Complex Fractions

Wow, thanks. Perfectly clear and fast on the reply to boot. Really appreciate it.
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October 29th, 2009, 04:06 PM   #4
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Re: Simplifying Complex Fractions

Hello, Tyster!


A complex fraction is one which has more than two "levels".

To simplify one, multiply numerator and denominator by the LCD of the denominators.





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[color=beige]. . [/color]and we've eliminated the messy part!

The rest is just "bookkeeping" . . . factor and reduce, if possible.






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November 3rd, 2009, 10:23 AM   #5
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Re: Simplifying Complex Fractions

I would multiply top and bottom of the complex fraction by ab yielding (a + b)/(a)^2(b)^2 which simplifies to 1/a(b)^2 + 1/b(a)^2.
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November 3rd, 2009, 01:47 PM   #6
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Re: Simplifying Complex Fractions

Since we are STILL doing homework here, I'd factor the bottom and simplify first. It's easier than first finding a LCD.
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