The correct statement for Mr. Knott's work is [tex]\frac{x - (x + 1)}{(x + 1) (x-1)}[/tex].
[tex]\frac{x}{x^2- 1} - \frac{1}{x - 1}[/tex]
The difference to the fractions given above is determined as follows;
[tex]\frac{x}{x^2- 1} - \frac{1}{x - 1} = \frac{x - (x + 1)}{(x + 1) (x-1)} = \frac{1}{x^2 - 1}[/tex]
From the solution above, we can use difference of two squares to expand "x² - 1"
x² - 1 = x² - 1² = (x + 1)(x - 1)
Thus, the correct statement for Mr. Knott's work is [tex]\frac{x - (x + 1)}{(x + 1) (x-1)}[/tex].
Learn more about simplification of mixed fractions here: https://brainly.com/question/1746829
