Question

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

Answer 1

multiply both sides by the denominator

Answer 2

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)

Answer 3

if you multiply both sides by the denominator you would get 1 + x > 0(1 - x)
which is 1 +x > 0

Answer 4

For some reason, I have to do this on paper, not in my head

Answer 5

you cannot multiply both sides by a variable in an inequality

Answer 6

@satellite: you can if you know that its gonna be +ve or -ve

Answer 7

I guess amogh it's right. Thanks guys.

Answer 8

np

Answer 9

??

Answer 10

your answer is all numbers between -1 and 1 i.e. (-1,1)

Answer 11

Okay, I give up

Answer 12

Satellite and amogh have the right idea.

Answer 13

f(x) ε (-1,1)

Answer 14

I neglected to use critical points and the intervals between them

Answer 15

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

Answer 16

Very usefull site! Thank ya all :)

Answer 17

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