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October 29th, 2009, 04:56 AM  #1 
Newbie Joined: Sep 2009 Posts: 8 Thanks: 0  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. 
October 29th, 2009, 05:25 AM  #2 
Senior Member Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0  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 
October 29th, 2009, 05:41 AM  #3 
Newbie Joined: Sep 2009 Posts: 8 Thanks: 0  Re: Simplifying Complex Fractions
Wow, thanks. Perfectly clear and fast on the reply to boot. Really appreciate it.

October 29th, 2009, 04:06 PM  #4 
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  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. [color=beige]. . [/color] [color=beige]. . [/color]and we've eliminated the messy part! The rest is just "bookkeeping" . . . factor and reduce, if possible. 
November 3rd, 2009, 10:23 AM  #5 
Member Joined: Oct 2009 Posts: 32 Thanks: 0  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.

November 3rd, 2009, 01:47 PM  #6 
Senior Member Joined: Mar 2007 Posts: 428 Thanks: 0  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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