Sum
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by. Find the fraction.
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Solution
Let the fraction be `x/(x + 3)`
When 1 is subtracted from both numerator and denominator, then the fraction be comes `(x - 1)/(x + 2)`
From the given information we have
`x/(x + 3) - 1/14 = (x - 1)/(x + 2) `
`(14x - x - 3)/(14(x + 3)) = (x - 1)/(x + 2)`
`(13x +- 3)/(14(x + 3)) = (x - 1)/(x + 2)`
`(13x - 3)(x + 2) = 14(x^2 + 28x - 42)`
`x^2 + 5x - 36 = 0`
`x^2 + 9x - 4x - 36 = 0`
x(x + 9)(x - 4) = 0
(x + 9)(x - 4) = 0
x = -9, 4
Since x cannot be negative So x = 4
Hence the fraction is `x/(x + 3) = 4/7`
Concept: Quadratic Equations
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