What's wrong with my approach?

GRE Quant Problem Solving
1

Unable to figure out why my approach gives the wrong answer to this Power Plus question.
Q: x > 1 : Quantitative Comparison Questions

Ans:

Cross multiply so we get
x(1-x) #### -x(x+1)
x-x^2 #### -x^2 -x
Add x^2 on both sides
x #### -x

The answer is A as it is just "X’ and x > 1
however, the correct answer is B. I was able to understand the other approach in the comments. But, I want to know why my approach is wrong.

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scroll down below to this comment.

All in all you don’t multiply or divide by negative values and In your case when you multiplied (1-x) to Qty A & (1-x) is a negative value as (x>1) is given. So, first you need to make that positive before multiplying. You can make \frac{-1}{1-x} positive by multiplying the numerator and the denominator by -1.

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3

Thank you for the solution!