What is the simplified form of 2 over x squared minus the quantity x minus 1 over x?

Answer 1

To simplify the expression ( \frac{2}{x^2} - \frac{x - 1}{x} ), first find a common denominator, which is ( x^2 ). Rewrite the second term: ( \frac{x - 1}{x} = \frac{(x - 1)x}{x^2} = \frac{x^2 - x}{x^2} ). Now, combine the fractions:

[ \frac{2 - (x^2 - x)}{x^2} = \frac{2 - x^2 + x}{x^2} = \frac{-x^2 + x + 2}{x^2}. ]

Thus, the simplified form is ( \frac{-x^2 + x + 2}{x^2} ).