To simplify the expression 2/x² + x – 1/x, we first need to find a common denominator. The common denominator for the terms in the expression is x². We will rewrite each term with this common denominator.
- The first term, 2/x², already has the denominator x².
- The second term, x, can be rewritten with the common denominator:
- x = x*x²/x² = x³/x²
- The third term, -1/x, can also be rewritten:
- -1/x = -1*x/x² = -x/x²
Now, substituting these rewritten terms back into the expression, we have:
2/x² + x – 1/x = 2/x² + x³/x² – x/x²
Next, we can combine the fractions over the common denominator:
(2 + x³ – x) / x²
This simplifies to:
(x³ + 1) / x²
So, the simplified form of the expression 2/x² + x – 1/x is:
(x³ + 1) / x²
This form retains the necessary details while presenting a clear and simplified version of the original expression.