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Answer
The simplified form is \( \frac{3x+2}{x^{2}} \).
Solution
Calculate or simplify the expression \( \frac{3}{x}+\frac{2}{x^{2}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{3}{x}+\frac{2}{x^{2}}\)
- step1: Reduce fractions to a common denominator:
\(\frac{3x}{x\times x}+\frac{2}{x^{2}}\)
- step2: Multiply the terms:
\(\frac{3x}{x^{2}}+\frac{2}{x^{2}}\)
- step3: Transform the expression:
\(\frac{3x+2}{x^{2}}\)
The simplified form of \( \frac{3}{x}+\frac{2}{x^{2}} \) is \( \frac{3x+2}{x^{2}} \).
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Simplify this solution Beyond the Answer
To simplify or manipulate the expression \( \frac{3}{x} + \frac{2}{x^{2}} \), we can find a common denominator, which would be \( x^2 \). This allows us to combine the fractions into a single fraction: \( \frac{3x}{x^2} + \frac{2}{x^2} = \frac{3x + 2}{x^2} \). This makes it easier to analyze the expression's behavior as \( x \) changes! By examining values for \( x \), you'll notice some interesting behavior! For instance, as \( x \) approaches 0, the expression approaches infinity; this points to a vertical asymptote at \( x = 0 \). Alternatively, as \( x \) gets larger, the expression behaves more linearly, emphasizing how fractions can vary greatly based on their inputs.
