Question
Real Tutor Solution
Tutor-Verified Answer
Answer
简化后的结果是 \(\frac{1 + 2x}{3x}\)。
Solution
首先将两个分数化为相同的分母：
\[
\frac{2}{5x} - \frac{1 - 10x}{15x}
\]
找到最小公倍数，分母为15x：
\[
\frac{2}{5x} = \frac{2 \times 3}{5x \times 3} = \frac{6}{15x}
\]
因此，表达式变为：
\[
\frac{6}{15x} - \frac{1 - 10x}{15x} = \frac{6 - (1 - 10x)}{15x} = \frac{6 - 1 + 10x}{15x} = \frac{5 + 10x}{15x}
\]
进一步约分：
\[
\frac{5 + 10x}{15x} = \frac{5(1 + 2x)}{15x} = \frac{1 + 2x}{3x}
\]
所以，简化后的结果是：
\[
\frac{1 + 2x}{3x}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To combine the fractions \( \frac{2}{5x} - \frac{1 - 10x}{15x} \), we first need a common denominator, which is \( 15x \). Rewrite the first fraction: \[ \frac{2}{5x} = \frac{2 \cdot 3}{5x \cdot 3} = \frac{6}{15x} \] Now substitute this back into our expression: \[ \frac{6}{15x} - \frac{1 - 10x}{15x} \] Now that we have a common denominator, we can combine the fractions: \[ \frac{6 - (1 - 10x)}{15x} = \frac{6 - 1 + 10x}{15x} = \frac{5 + 10x}{15x} \] To simplify, we can factor out the 5 from the numerator: \[ \frac{5(1 + 2x)}{15x} = \frac{1 + 2x}{3x} \] Thus, the final simplified result is: \[ \frac{1 + 2x}{3x} \]
