# The numerator of

Let the denominator be ‘a’.

Numerator = a – 3

[As numerator is 3 less than denominator]Now, if 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is .

20(a2 – a – 6) + 20a2 – 20a = 29a2 + 58a

11a2 – 98a – 120 = 0

11a2 – 110a + 12a – 120 = 0

11a(a – 10) + 12(a – 10) = 0

(11a + 12)(a – 10) = 0

a = 10 or a = -12/11
Since, denominator can't be a fraction
⇒ a = 10

and numerator = a - 3 = 10 - 3 = 7

Thus the original fraction is 7/10.

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