# 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 Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Get To Know About Quadratic Formula42 mins  Quiz | Knowing the Nature of Roots44 mins  Take a Dip Into Quadratic graphs32 mins  Foundation | Practice Important Questions for Foundation54 mins  Nature of Roots of Quadratic Equations51 mins  Getting Familiar with Nature of Roots of Quadratic Equations51 mins  Quadratic Equation: Previous Year NTSE Questions32 mins  Understand The Concept of Quadratic Equation45 mins  Champ Quiz | Quadratic Equation33 mins  Balance the Chemical Equations49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 