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Given the fraction ab, if n times the denominator is subtracted from the numerator and n times the numerator from the denominator, 2 is obtained, then said fraction in terms of n will be

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Answer to a math question Given the fraction ab, if n times the denominator is subtracted from the numerator and n times the numerator from the denominator, 2 is obtained, then said fraction in terms of n will be

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Sigrid
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120 Answers
\text{1. Start with the fraction } \frac{a}{b} \text{ and set up the given condition:} \\\frac{a - nb}{b - na} = 2

\text{2. Cross-multiply to clear the fraction: } \\a - nb = 2(b - na)

\text{3. Distribute and simplify both sides:} \\a - nb = 2b - 2na

\text{4. Rearrange to collect all terms involving } a \text{ on one side and terms involving } b \text{ on the other:} \\a + 2na = 2b + nb

\text{5. Factor out common factors from both sides: } \\a(1 + 2n) = b(2 + n)

\text{6. Isolate } \frac{a}{b} \text{:} \\\frac{a}{b} = \frac{2 + n}{1 + 2n}

\text{7. Therefore, the fraction } \frac{a}{b} \text{ in terms of } n \text{ is } \frac{2 + n}{1 + 2n}

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