# The numerator of a fraction is one more than its denominator. If its reciprocal is added to it the sum is . Find the fraction.

Let the denominator be ‘X’, so the numerator will be ‘(X+1)’.

the fraction is

On simplifying further,

30(2X2 + 2X + 1) = 61 (X2 + X)

60X2 + 60X + 30 = 61X2+ 61X

X2 + X – 30 = 0–––––– (i)

On applying Sreedhracharya formula

X= – 6 or 5

X = 5 (Only positive values)

Denominator is = 5 & numerator is (X+1) = 6

The fraction is .

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