Q. 264.0( 3 Votes )

The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is . Find the fraction.

Answer :

Let the numerator be x

Denominator = x + 3


Original number =



On taking the LCM




{ using (a + b)2 = a2 + 2ab + b2}



29x2 + 87x = 20x2 + 60x + 90


9x2 + 27x – 90 = 0


9(x2 + 3x – 10) = 0


x2 + 3x – 10 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 3 c = – 10


= 1. – 10 = – 10


And either of their sum or difference = b


= 3


Thus the two terms are 5 and – 2


Difference = 5 – 2 = 3


Product = 5. – 2 = – 10


x2 + 5x – 2x – 10 = 0


x(x + 5) – 2(x + 5) = 0


(x + 5)(x – 2) = 0


(x + 5) = 0 or (x – 2) = 0


x = 2 or x = – 5


x = 2 (rejecting the negative value)


So numerator is 2


Denominator = x + 3 = 2 + 3 = 5


So required fraction is 2/5


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