Question

Find all numbers x for which \[\frac{1}{x}+\frac{1}{1-x} > 0\]

Answer 1

hard? :)

Answer 2

\[\frac{1-x+x}{x(1-x)} >0\]
\[\frac{1}{x(1-x)} >0\]
\[f(x)=\frac{1}{x(1-x)} \text{ is undefined at x=0 & x=1 }\]


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0 1

We need to choose a number from the following intervals:
(-inf,0) ; (0,1) ; (1,inf)
/\ /\ /\
| | |
-1 .5 2


f(-1)=-
f(.5)=+
f(2)=-

We want to know where f>0
so f>0 on the interval (0,1)

Answer 3

Nope I just wanted to explain it :)

Answer 4

thanks I was solving this one but I couldn't figure out why my answer was different from the given answer

Answer 5

did you try to clear the denominators?

Answer 6

I just thought that it was postive if both numerator and denominator are positive, or both are negative

Answer 7

The bad thing about clearing the denominators is that x is not always greater than 0
and 1-x is not always positive so we can't just simply multiply both sides by x and (1-x)

Answer 8

right.

Answer 9

Did you right it as one fraction like i did?

Answer 10

Or did you look at the fractions separately?

Answer 11

right=write my bad