Q. 274.3( 7 Votes )

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by . Find the fraction.

Answer :

Let the denominator of required fraction be x

Numerator of required fraction be = x – 3


Original number =


If 1 is added to the denominator, then the new fraction will become


According to the given condition,







x2 + x = 15x – 45


x2 – 14x + 45 = 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 = – 14 c = 45


= 1.45 = 45


And either of their sum or difference = b


= – 14


Thus the two terms are – 9 and – 5


Sum = – 9 – 5 = – 14


Product = – 9. – 5 = – 45


x2 – 14x + 45 = 0


x2 – 9x – 5x + 45 = 0


x(x – 9) – 5(x – 9) = 0


(x – 9)(x – 5) = 0


x = 9 or x = 5


Case I: x = 5



Case II: x = 9


(Rejected because this does not satisfy the condition given)


Hence the required fraction is


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