# What is the LCD for this complex fraction?

• Apr 12th 2009, 06:43 PM
Hapa
What is the LCD for this complex fraction?
x + 2 - (12 / x + 3) / x - 5 + (16 / x + 3)

Would the LCD be x(x + 3)? If so, I just multiply the numerator and denominator of this complex fraction by x(x + 3) to find the answer, correct?

Thanks again!
• Apr 12th 2009, 06:50 PM
mollymcf2009
Quote:

Originally Posted by Hapa
x + 2 - (12 / x + 3) / x - 5 + (16 / x + 3)

Would the LCD be x(x + 3)? If so, I just multiply the numerator and denominator of this complex fraction by x(x + 3) to find the answer, correct?

Thanks again!

First let me make sure that I have the right problem:

$\frac{x + 2 - (\frac{12}{x+3})}{x - 5 + (\frac{16}{x+3})}$

Is this what it looks like? Or, in the parentheses is it $(\frac{12}{x} + 3)$?
• Apr 12th 2009, 06:55 PM
Hapa
Molly,

Your first interpretation is correct. My apologies for the confusion.
• Apr 12th 2009, 07:06 PM
Prove It
Are you trying to simplify this? Or are you just finding an LCM?
• Apr 12th 2009, 07:07 PM
mollymcf2009
Quote:

Originally Posted by Hapa
Molly,

Your first interpretation is correct. My apologies for the confusion.

No problem, it happens all the time. Ok, the first thing you should do is get a LCD in the top and bottom of the larger fraction:

$
\frac{x + 2 - (\frac{12}{x+3})}{x - 5 + (\frac{16}{x+3})}$

The LCD in both the top and bottom will be (x+3). Think of the non-fraction numbers as $\frac{number}{1}$, this will help you see how to evaluate their LCD

So you will have a fraction over a fraction, with LCD both (x+3). Then, just multiply the top by the reciprocal of the bottom to get rid of the big fraction. This will leave you with a new fraction, which you can multiply out giving you your final LCD

Good luck! (Wink)
• Apr 12th 2009, 07:08 PM
Hapa
I am trying to simplify this complex fraction.
• Apr 12th 2009, 07:08 PM
Prove It
Quote:

Originally Posted by mollymcf2009
No problem, it happens all the time. Ok, the first thing you should do is get a LCD in the top and bottom of the larger fraction:

$
\frac{x + 2 - (\frac{12}{x+3})}{x - 5 + (\frac{16}{x+3})}$

The LCD in both the top and bottom will be (x+3)

So you will have a fraction over a fraction, with LCD both (x+3). Then, just multiply the top by the reciprocal of the bottom to get rid of the big fraction. This will leave you with a new fraction, which you can multiply out giving you your final LCD

Good luck! (Wink)

Just so there's no confusion...

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b}\div\frac{c}{d}$

$= \frac{a}{b}\times \frac{d}{c}$.
• Apr 13th 2009, 04:23 AM
stapel
Quote:

Originally Posted by Hapa
I am trying to simplify this complex fraction.

To learn the methodology, try studying one or two online lessons covering how to simplify complex fractions. Make sure you can follow the worked examples. :D