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# easy inequality Watch

1. I am trying to show that if 0<a<1 and 0<b<1 and we know that a is less than b then:

I have simplified the fractions to:

but I can't see how this is less than 0.5
2. Your best bet is to multiply through by the denominators of the two fractions to get (we can do this since everything is positive). Why must this be true?
3. That must be true because b<1?

but is that not using the fact that it is less than a half without having shown it?
4. 2ab + a < b

Should be false. Take a = 1/2 and b arbitrary in (1/2,1).
5. so do you mean that it the inequality in the op is not true?
6. (Original post by sonic7899)
so do you mean that it the inequality in the op is not true?
Unless 1/2 < 0 it's false.
7. (Original post by DeanK22)
Unless 1/2 < 0 it's false.
Erm I think I made a mistake in my workings. The fraction I should be showing is less than a half is actually:

8. (Original post by sonic7899)
Erm I think I made a mistake in my workings. The fraction I should be showing is less than a half is actually:

That makes more sense. You need to use the fact that .
9. (Original post by sonic7899)
Erm I think I made a mistake in my workings. The fraction I should be showing is less than a half is actually:

In which case, nuodai's suggestion is the way to go here. What is the original question?
10. (Original post by nuodai)
That makes more sense. You need to use the fact that .
Ah I think I have just got it. Is is just that a<b and so:

?
11. (Original post by sonic7899)
Ah I think I have just got it. Is is just that a<b and so:

?
Seems fine to me

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Updated: December 5, 2010
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