simplifying fractions by common denomonators

• Jul 14th 2011, 02:48 AM
canger
simplifying fractions by common denomonators
Hello,

I was wondering if there is any way to simplify

$\displaystyle \frac{1}{(x^3 + 2)^7} -\frac{(x^3 + 2)^7}{(x^8 + 12)^6}$

Thanks!
• Jul 14th 2011, 03:25 AM
Prove It
Re: simplifying fractions by common denomonators
You could always start by getting a common denominator...
• Jul 14th 2011, 08:53 PM
canger
Re: simplifying fractions by common denomonators
I can't figure out how to get lowest common denominator.
I'm confused because of the powers.
• Jul 14th 2011, 08:56 PM
mr fantastic
Re: simplifying fractions by common denomonators
Quote:

Originally Posted by canger
I can't figure out how to get lowest common denominator.
I'm confused because of the powers.

The LCD is (x^3 + 2)^7 (x^8 + 12)^6.
• Jul 14th 2011, 09:09 PM
canger
Re: simplifying fractions by common denomonators
So what about the LCD for $\displaystyle {-\frac{(x^2 + 1)^{\frac{1}{2}}}{(x^2 +4)} + {\frac{1}{(x^2 + 1)^{\frac{1}{2}}}}}$
Can you do anything better with that one?
• Jul 14th 2011, 09:14 PM
mr fantastic
Re: simplifying fractions by common denomonators
Quote:

Originally Posted by canger
So what about the LCD for $\displaystyle {-\frac{(x^2 + 1)^{\frac{1}{2}}}{(x^2 +4)} + {\frac{1}{(x^2 + 1)^{\frac{1}{2}}}}}$
Can you do anything better with that one?

Well, what do you think a common denominator is? Then I'll tell you if you can do 'better' ....
• Jul 14th 2011, 09:22 PM
canger
Re: simplifying fractions by common denomonators
Do I have to work out the square root of $\displaystyle x^2 + 1$? Because that would bring complex numbers into it, wouldn't it? And we aren't covering those in my course.
Otherwise, how can I multiply these terms when they aren't the same? It's just the $\displaystyle x^2$ that's the same...?
• Jul 15th 2011, 01:54 PM
mr fantastic
Re: simplifying fractions by common denomonators
Quote:

Originally Posted by canger
Do I have to work out the square root of $\displaystyle x^2 + 1$? Because that would bring complex numbers into it, wouldn't it? And we aren't covering those in my course.
Otherwise, how can I multiply these terms when they aren't the same? It's just the $\displaystyle x^2$ that's the same...?

Look at what was done in post #4.