The sum of the nermerator and denominator of a fraction greater by `1` than thrice the numerator. If the numerator decreased by `1`, then the fraction reduces to `(1)/(3)`. Find the fraction

Explanation

Let the numerator of the fraction be `x` and it denominator `y`.
Then the fraction is `(x)/(y)`.
From the first condition,
`x=y=3x+1`
`:.-2x+y=1`…..`(1)`
From the second condition,
`{:((x-1)/(y)=(1)/(3), :. 3x-3=y):}`
`:.3x-y=3`.....`(2)`
Adding equation `(1)` and `(2)`,
`{:(-2x+y=1" ...(1)"),(3x-y=3" ...(2)"),(bar(""""x" "="4)):}`
Substituting `x=4` in equation `(1)`.
`{:(-2(4)+y=1, :.-8+y=1, :.y=1+8, :.y=9):}`