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.

Answer :

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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