# 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:

Or

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