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Simplify the complex fraction \[ \begin{array}{l}\frac{\frac{x+2}{4}}{\frac{5 x-1}{8}} \\ \frac{\frac{x+2}{4}}{\frac{5 x-1}{8}}=\square\end{array} \]

Ask by Harrington Park. in the United States
Jan 22,2025

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The simplified form is \( \frac{2x+4}{5x-1} \).

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Bonus Knowledge

To simplify the complex fraction \[ \frac{\frac{x+2}{4}}{\frac{5 x-1}{8}}, \] we can multiply by the reciprocal of the denominator. This means we take the numerator and multiply it by the reciprocal of the denominator. First, we set it up like this: \[ \frac{x+2}{4} \div \frac{5x-1}{8} = \frac{x+2}{4} \times \frac{8}{5x-1}. \] Now, we can multiply the fractions: \[ = \frac{(x+2) \cdot 8}{4 \cdot (5x-1)}. \] This simplifies to: \[ = \frac{8(x + 2)}{4(5x - 1)}. \] Next, we can simplify the division by 4: \[ = \frac{2(x + 2)}{5x - 1}. \] Thus, the simplified form of the complex fraction is \[ \frac{2(x + 2)}{5x - 1}. \]

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