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X negative 1 over x squared plus 1 over x

Sagot :

Answer:

To simplify the expression \( \frac{-1}{x^2} + \frac{1}{x} \), follow these steps:

1. Find a Common Denominator

The common denominator for the terms \(\frac{-1}{x^2}\) and \(\frac{1}{x}\) is \(x^2\).

2. Rewrite Each Term with the Common Denominator

- For \(\frac{-1}{x^2}\), the denominator is already \(x^2\), so it remains \(\frac{-1}{x^2}\).

- For \(\frac{1}{x}\), rewrite it with \(x^2\) as the denominator:

 \[

 \frac{1}{x} = \frac{1 \cdot x}{x \cdot x} = \frac{x}{x^2}

 \]

3. Combine the Terms

Now that both terms have the same denominator, combine them:

\[

\frac{-1}{x^2} + \frac{x}{x^2} = \frac{-1 + x}{x^2}

\]

Simplified Expression

The simplified expression is:

\[

\frac{x - 1}{x^2}

\]