The numerator of a fraction is one more than its denominator. If its reciprocal is subtracted from it, the difference is 11/30 . Find the fraction.

Question

The numerator of a fraction is one more than its denominator. If its reciprocal is subtracted from it, the difference is \(\frac{11}{30}.\) Find the fraction.

Answer 1

Let the denominator of the fraction be x. Then, the numerator = x + 1

∴ Given fraction = \(\frac{x+1}{x};\) Its reciprocal = \(\frac{x}{x+1}\)

According to the question, \(\frac{x+1}{x}-\)\(\frac{x}{x+1}\) = \(\frac{11}{30}\)

If x = 5, x +1 = 6

Hence the given fraction = \(\frac65\)

∴ The fraction is \(\frac65\) or \(-\frac56\)