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Alexis1994_13 Group Title

(1+x)/(1-x)>0 What's next? :S

  • 3 years ago
  • 3 years ago

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  1. heromiles Group Title
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    multiply both sides by the denominator

    • 3 years ago
  2. amogh Group Title
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    you cannot do that as 1-x can be negative, You can do that be wavy curve method, Or common sense, If a ratio has to be +ve, both numerator n denominator have to be of the same sign, 1+x >0 , x>-1 1-x >0 , x<1 common soln. (-1,1) 1+x<0 , x<-1 1-x<0 , x>1 common soln. (nothing!) Therefore, the ans is (-1,1)

    • 3 years ago
  3. joemath314159 Group Title
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    if you multiply both sides by the denominator you would get 1 + x > 0(1 - x) which is 1 +x > 0

    • 3 years ago
  4. heromiles Group Title
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    For some reason, I have to do this on paper, not in my head

    • 3 years ago
  5. satellite73 Group Title
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    you cannot multiply both sides by a variable in an inequality

    • 3 years ago
  6. amogh Group Title
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    @satellite: you can if you know that its gonna be +ve or -ve

    • 3 years ago
  7. Alexis1994_13 Group Title
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    I guess amogh it's right. Thanks guys.

    • 3 years ago
  8. amogh Group Title
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    np

    • 3 years ago
  9. satellite73 Group Title
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    ??

    • 3 years ago
  10. satellite73 Group Title
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    your answer is all numbers between -1 and 1 i.e. (-1,1)

    • 3 years ago
  11. heromiles Group Title
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    Okay, I give up

    • 3 years ago
  12. joemath314159 Group Title
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    Satellite and amogh have the right idea.

    • 3 years ago
  13. Alexis1994_13 Group Title
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    f(x) ε (-1,1)

    • 3 years ago
  14. heromiles Group Title
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    I neglected to use critical points and the intervals between them

    • 3 years ago
  15. satellite73 Group Title
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    and it is easy enough to solve. for one thing you can just think of \[(1+x)(1-x)> 0\] which is a parabola facing down. therefore it is positive between the zeros and negative outside of them. the zeros are -1 and 1 so it is positive between those two numbers and negative outside of them

    • 3 years ago
  16. Alexis1994_13 Group Title
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    Very usefull site! Thank ya all :)

    • 3 years ago
  17. satellite73 Group Title
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    or you can say you have two factors , 1+x which is positive if x > -1 negative for x < -1 1-x which is positive if x < 1 and negative is x > 1 then what happens when you divide? if you are between -1 and 1 both are positive, and so the quotient will be as well

    • 3 years ago
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