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21. \( \frac{x^{2}}{x^{2}+x} \)

Ask by Hodgson Barber. in the United States
Mar 12,2025

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The simplified form is \( \frac{x}{x+1} \).

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Let's explore a useful transformation of the expression \( \frac{x^{2}}{x^{2}+x} \). By factoring the denominator, we can rewrite it as \( \frac{x^{2}}{x(x+1)} \). This is particularly handy when simplifying or calculating limits, as it clearly shows how the values interact as \( x \) approaches certain points, like zero. Now, if we plug in some specific values for \( x \), say \( x = 0 \) and \( x = -1 \), we'll find interesting results. For \( x = 0 \), the expression evaluates to 0, while for \( x = -1 \), we hit a division by zero scenario. This illustrates the importance of identifying domain restrictions in rational expressions.

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