The numerator of a fraction is 3 less than its denominator.If 11 is added to the denominator,the fraction is decreased by `1/15` Find the fraction

Answer

`(2)/(5)`

Explanation

Let the required fraction in simplest from be `(x-3)/(x)`, Then,
`(x-3)/(x)-(x-3)/(x+1)=(1)/(15)implies(x-3)[(1)/(x)-(1)/(x+1)]=(1)/(15)`
`:." "15(x-3)=x(x+1)impliesx^(2)-14x+45=0impliesx=5" or "x=9.`
So, the required fraction is `(2)/(5)." "["neglecting "(6)/(9)]`