9. The numerator of a fraction is 2 less thanits denominator. If 3 is

1.	9. The numerator of a fraction is 2 less thanits denominator. If 3 is added to each of thenumerator and the denominator, the fractionincreases by 1/18 find the fraction.
Answer» *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 $\frac{10}{12} \: or \: \frac{ - 11}{ - 9}$ $= \frac{11}{9}$