Thread: Rationalizing Denominator

Doing some simple antiderivatives and I wanted to rationalize the denominator of one of the questions to eventually expand the expression:

QUESTION: (2 + x^2)/(1 + x^2), find the antiderivative

*So i mulitiplied the expression by (1-x^2)/(1-x^2) which is technically = to 1

*I ended up with 1 - x^4 in the denominator still and it seems i'm unable to cancel this, I was meaning to end up with my expression all over 1

Am I rationalizing the denominator correctly? Or in this particular question are u unable to rationalize the denominator?

Thanks!

Originally Posted by FinkieMufu

Or in this particular question are u unable to rationalize the denominator?

Right, because it's already rational!

You're expected to do long division or else the numerator give-and-take manouvre. I.e. re-write the numerator as 1 + x^2 + 1, and you should be able to see a good place to split the fraction into two...

Originally Posted by FinkieMufu

Doing some simple antiderivatives and I wanted to rationalize the denominator of one of the questions to eventually expand the expression:
QUESTION: (2 + x^2)/(1 + x^2), find the antiderivative

It is simply $\displaystyle \int {\frac{{2 + x^2 }}{{1 + x^2 }}dx = \int {\left( {1 + \frac{1}{{1 + x^2 }}} \right)dx} } $.

There is nothing to rationalize.