Q. 175.0( 3 Votes )
The numerator of a fraction is one more than its denominator. If its reciprocal is subtracted from it, the difference is . Find the fraction.
Given: Numerator of a fraction is one more than its denominator.
To Find: The fraction
Assumption: Let the denominator be x.
Numerator = x + 1
Therefore, the fraction
From the second case, we get,
Taking L.C.M we get,
Cross-multiplying we get,
30(2x + 1) = 11(x2 + x)
60x + 30 = 11x2 + 11x
11x2 + 11x – 60x – 30 = 0
11x2 – 49x – 30 = 0
Now, we need to factorise such that, on multiplication we get 330 and on substraction we get 49.
Therefore, 55 and 6 can be the factors.
So, equation becomes,
11x2 – (55x – 6x) – 30 = 0
11x2 – 55x + 6x – 30 = 0
11x(x – 5) + 6(x – 5) = 0
(11x + 6)(x – 5) = 0
So, 11x + 5 = 0 or x – 5 = 0
So the possible fractions are:
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