marus
What mathematical rule does it govern?
\(\frac{x+1}{1-x}= \frac{x+1}{-(1-x)} = \frac{x+1}{x-1}\)
I'm not quite sure I understand your question, but the equation above isn't right. The first fraction is not equal to the second - in fact, it's exactly equal to the negative of the second. The second and third fractions are equal.
marus
How is it possible to multiply an expression in the divisor by (-1) and change the order of units?
There is no 'order' when you're adding numbers; a+b is the same thing as b+a. By the same token, x-1 is the same thing as -1+x. If we want, we can factor out -1; when we do, we'll need to 'flip' all of the signs in the brackets. So -(1 - x) is equal to -1 + x, as you can confirm by expanding -(1 - x). So the following four expressions are all equal:
\(x - 1 = -1 + x = -(1 - x) = -(-x + 1)\)