Question
Rewrite the expression using the common denominator: \( \frac{2 x}{x}+\frac{3}{x^{2}} \) \( \frac{1}{x^{2}}+\frac{3}{x^{2}} \) \( \frac{2 x}{x^{2}}+\frac{3}{x^{2}} \) DONE
Ask by Ayala Erickson. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \( \frac{2x}{x}+\frac{3}{x^{2}} \) can be rewritten as \( \frac{2x^{2}+3}{x^{2}} \).
Solution
Calculate or simplify the expression \( \frac{2x}{x}+\frac{3}{x^{2}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{2x}{x}+\frac{3}{x^{2}}\)
- step1: Reduce the fraction:
\(2+\frac{3}{x^{2}}\)
- step2: Reduce fractions to a common denominator:
\(\frac{2x^{2}}{x^{2}}+\frac{3}{x^{2}}\)
- step3: Transform the expression:
\(\frac{2x^{2}+3}{x^{2}}\)
The expression \( \frac{2x}{x}+\frac{3}{x^{2}} \) can be rewritten as \( \frac{2x^{2}+3}{x^{2}} \).
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Simplify this solution Bonus Knowledge
To combine the fractions, we need a common denominator. The least common denominator here is \( x^2 \). Rewriting \( \frac{2x}{x} \) with \( x^2 \) as the denominator gives us \( \frac{2x \cdot x}{x \cdot x} = \frac{2x^2}{x^2} \). Now we can combine it with \( \frac{3}{x^2} \). So, \( \frac{2x^2}{x^2} + \frac{3}{x^2} = \frac{2x^2 + 3}{x^2} \). The final expression, all tidy and ready for action, is \( \frac{2x^2 + 3}{x^2} \). You're all set!
