Question

Carlos wants to make a scale drawing of a rectangle. he wants the rectangle to have a length of (x-1) units and an area of 1-x/x^2+1 square units. What can you say about how wide the rectangle should be? Explain.

Answer 1

I will assume you want the area to be
(1-x)/(x^2 +1)

area = l x w
so (1-x)/(x^2 + 1 ) = w(x-1)
w = [ (1-x)/(x^2 + 1) ] / (x-1)
= -1/(x^2 + 1)

What I would say is "There is no real number for the width"

-since x^2 is always positive, then x^2 + 1 is always positive
Thus -1/(a positive) = a negative
We cannot have a negative width

unless you want your typed version to have a different meaning besides my interpretation.
the way you typed it it would have a value of 2 - 1/x
and I am pretty sure you didn't mean that.