jamesk486 wrote:x is not 1, (1-x^5)/(1-x) < 1/1-x
(1) x>0
(2) x<1

using (1-x^5)/(1-x) < 1/1-x
=> (1/1-x) - (x^5/1-x) < 1/1-x
=> -x^5/(1-x)<0
=> multiplying each side by (1-x)^2 since its positive
=> -x^5(1-x) which is also x^5*(x-1)<0
=> dividing each side by x^4, we get x(x-1)<0, so the answer must be c

but what if from -x^5/(1-x)<0, is it possible to mulitply each side by (-1) to get x^5/(1-x) >0?
for some reason if i do it that way my answer comes out differently..

(the answer is C btw)

Your working is perfect. Solution of the given inequality are the two statements taken together.

But, even if you mulitply each side by (-1) to get x^5/(1 - x) > 0, the result remains same. Can you show us your working?

In fact

x^5/(1 - x) > 0 when multiplied by (1 - x) ^2 becomes x^5 (1 - x) > 0 and then a division by x^4 leads it to x (1 - x) > 0, which is possible when both factors are with same sign. Both negative would prove to be an invalid consideration, and both positive gets us

x > 0 and 1 - x > 0, which translates to the same [spoiler]0 < x < 1.

C[/spoiler]