A seven and a lot of twos, nines and sixes

Let:

$x=7.\overline { 296 }$

Multiply both sides by $1000$ :

$1000x=7296.\overline { 296 }$

Subtract by $x$ in order to remove the $.\overline { 296 }$ :

$1000x=7296.\overline { 296 } \\ \underline { -\quad \quad x=7.\overline { 296 } } \\ \quad 999x=7289$

$\Large \frac { 999x }{ 999 } =\frac { 7289 }{ 999 }$

$\Large x=\frac { 7289 }{ 999 }$

In lowest terms:

$\Large \frac { 7289 }{ 999 } =\frac { 197 }{ 27 } =\frac { m }{ n }$

$m-n$

$197-27=\boxed { 170 }$