We already have calculator for Gaussian elimination on this site, it is here Gaussian elimination. However, it does all calculations with floating point numbers. Sometimes this loses the precision, which could be an issue.
This calculator retains fractions on all calculation stages. So, at the end, it is possible to get result in fraction form - with numerator and denominator. I use "solution vector as fractions" to output it. Top row is numerators, and bottom row is denominators.