Q21 of 47 Page 1

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is . Find the original fraction.

Let the denominator of the original fraction be x.

Given that the numerator is 3 less, So numerator = x-3


So,


Now, 2 is added to both numerator and denominator,


So,



⇒ ⇒


⇒ 20(2x2-2x-6) = 29(x2 + 2x)


⇒ 40x2-40x-120 = 29x2 + 58x


⇒ 11x2-98x-120 = 0


⇒ 11x2-110x + 12x-120 = 0


⇒ 11x(x-10) + 12(x-10) = 0


⇒ (x-10)(11x + 12) = 0


⇒ x = 10 or (rejected)


So original fraction =


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