Question

First we increase the denominator of a positive fraction by 3 and next time we decrease it by 5. The sum of the resulting fractions proves to be equal to 2/3 . Find the denominator of the fraction if its numerator is 2 .

Answer 1

$\bold{Let \: the \: fraction \: be = \frac{2}{a} }$

From the given conditions

$\bold{ \frac{2}{a + 3} + \frac{2}{a - 5} = \frac{2}{3} ⟹ \frac{2a - 2}{(a + 3)(a - 5)} = }$

$\bold{ \frac{1}{3} ⟹ {a}^{2} - 2a - 15 = 6a - 6⟹ {a}^{2} - 8a - 9 = 0⟹a = 9 ,- 1}$

As the fraction is positive the denominator will be 9