# Fraction Simplification

## Homework Statement

How do I simplify the following

$$\frac{\sqrt[3]{m^2+m} . \sqrt{1+m^2}}{\sqrt{1+m^2}.\sqrt{1+m^2}}$$

## The Attempt at a Solution

I know that the denominator will be $$1+m^2$$ but I don't know how to simplify the numerator. Can anyone show me how?

## Answers and Replies

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Try writing out the powers as a fraction. That is, let the square roots be ^(1/2) and such. It'll be easier to see as you just add the fractions.

Try writing out the powers as a fraction. That is, let the square roots be ^(1/2) and such. It'll be easier to see as you just add the fractions.
It doesn't seem to change much

$$\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}$$

Should we just add the powers, and what about the terms?

Last edited:
What's 1/3 + 1/2?

Mark44
Mentor
What's 1/3 + 1/2?
I don't see how that is applicable in this problem. If I'm understanding you correctly, you are trying to convince us that a1/3b1/2 can somehow be combined.

Mark44
Mentor
It doesn't seem to change much

$$\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}$$

Should we just add the powers, and what about the terms?
I think this is about all you can do by way of simplification. The two factors in the numerator have different bases, so can't be combined.

Matterwave