# Thread: simplifying fractions by common denomonators

1. ## simplifying fractions by common denomonators

Hello,

I was wondering if there is any way to simplify

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

Thanks!

2. ## Re: simplifying fractions by common denomonators

You could always start by getting a common denominator...

3. ## Re: simplifying fractions by common denomonators

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

4. ## Re: simplifying fractions by common denomonators

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.

5. ## Re: simplifying fractions by common denomonators

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

6. ## Re: simplifying fractions by common denomonators

Originally Posted by canger
So what about the LCD for ${-\frac{(x^2 + 1)^{\frac{1}{2}}}{(x^2 +4)} + {\frac{1}{(x^2 + 1)^{\frac{1}{2}}}}}$
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' ....

7. ## Re: simplifying fractions by common denomonators

Do I have to work out the square root of $x^2 + 1$? 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 $x^2$ that's the same...?

8. ## Re: simplifying fractions by common denomonators

Originally Posted by canger
Do I have to work out the square root of $x^2 + 1$? 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 $x^2$ that's the same...?
Look at what was done in post #4.