Fraction Addition - Algorithm

$1.$ Start with result $= 0/1$ (numerator $= 0$, denominator $= 1$).

$2.$ Parse each fraction from the string (handle $+$ and $-$ signs).

$3.$ For each fraction $\frac{a}{b}$, compute new numerator $= num \times b + a \times denom$ and new denominator $= denom \times b$.

$4.$ After each addition, simplify using GCD.