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Fraction Simplification

  • Thread starter math2010
  • Start date
  • #1
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Homework Statement



How do I simplify the following

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


The Attempt at a Solution



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

Answers and Replies

  • #2
354
2
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.
 
  • #3
19
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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.
It doesn't seem to change much

[tex]\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}[/tex]

Should we just add the powers, and what about the terms?
 
Last edited:
  • #4
354
2
What's 1/3 + 1/2?
 
  • #5
33,162
4,847
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.
 
  • #6
33,162
4,847
It doesn't seem to change much

[tex]\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}[/tex]

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.
 
  • #7
Matterwave
Science Advisor
Gold Member
3,965
326
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.
 

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