# The denominator of a fraction exceeds its numerator by 3. If 3 is added to both numerator and denominator, the difference between the new and the original fraction is . Find the original fraction.

Let the denominator be ‘(X+3)’, so the numerator will be ‘X’.

the original fraction is

the new fraction is

On simplifying further,

88(9) = 9(X2 + 9X + 18)

X2 + 9X – 70 = 0 –––––– (i)

On applying Sreedhracharya formula

X = –14 or 5.

the numerator is X = 5 and denominator (X+3) will be 8 and the fraction will be , as taking (–14) will form a fraction i.e., (not satisfying the conditions) .

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