Question

9. The numerator of a fraction is 2 less than
its denominator. If 3 is added to each of the
numerator and the denominator, the fraction
increases by 1/18 find the fraction.
​

Answer 1

Let the denominator of the required fraction be x.

-> Numerator will be x - 2.

According to the condition,

$\frac{x - 2 + 3}{x + 3} = \frac{x - 2}{x} + \frac{1}{18}$

$= > \frac{x + 1}{x + 3} - \frac{x - 2}{x} = \frac{1}{18}$

$= > {x}^{2} - 3x - 108 = 0$

$= > {x}^{2} - 12x + 9x - 108 = 0$

$- > (x - 12)(x + 9) = 0$

$x = 12 \: or \: x = - 9$

Therefore the required fraction is

$\frac{10}{12} \: or \: \frac{ - 11}{ - 9}$

$= \frac{11}{9}$