# Fraction Simplification

• math2010

## 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?

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?

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What's 1/3 + 1/2?

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.

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.

Are you sure the first term is m^2+m not m^3+m? cus then, you could factor out an m and go from there.

Otherwise, I see no way of simplifying this expression other than canceling out one sqrt(1+m^2) from top and bottom.