[tex]\frac{3}{7}[/tex] is the original fraction
let the denominator of the original fraction be n, then
[tex]\frac{n-4}{n}[/tex] is the original fraction
adding 2 to the numerator gives
[tex]\frac{n-4+2}{n}[/tex] = [tex]\frac{5}{7}[/tex], hence
[tex]\frac{n-2}{n}[/tex] = [tex]\frac{5}{7}[/tex] ( cross- multiply )
7(n - 2) = 5n
7n - 14 = 5n ( subtract 5n from both sides )
2n - 14 = 0 ( add 14 to both sides )
2n = 14 ( divide both sides by 2 )
n = 7
original fraction = [tex]\frac{7-4}{7}[/tex] = [tex]\frac{3}{7}[/tex]
