<p>Given a string <code>expression</code> representing an expression of fraction addition and subtraction, return the calculation result in string format.</p>

<p>The final result should be an <a href="https://en.wikipedia.org/wiki/Irreducible_fraction" target="_blank">irreducible fraction</a>. If your final result is an integer, change it to the format of a fraction that has a denominator <code>1</code>. So in this case, <code>2</code> should be converted to <code>2/1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;-1/2+1/2&quot;
<strong>Output:</strong> &quot;0/1&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;-1/2+1/2+1/3&quot;
<strong>Output:</strong> &quot;1/3&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;1/3-1/2&quot;
<strong>Output:</strong> &quot;-1/6&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The input string only contains <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>, <code>&#39;/&#39;</code>, <code>&#39;+&#39;</code> and <code>&#39;-&#39;</code>. So does the output.</li>
	<li>Each fraction (input and output) has the format <code>&plusmn;numerator/denominator</code>. If the first input fraction or the output is positive, then <code>&#39;+&#39;</code> will be omitted.</li>
	<li>The input only contains valid <strong>irreducible fractions</strong>, where the <strong>numerator</strong> and <strong>denominator</strong> of each fraction will always be in the range <code>[1, 10]</code>. If the denominator is <code>1</code>, it means this fraction is actually an integer in a fraction format defined above.</li>
	<li>The number of given fractions will be in the range <code>[1, 10]</code>.</li>
	<li>The numerator and denominator of the <strong>final result</strong> are guaranteed to be valid and in the range of <strong>32-bit</strong> int.</li>
</ul>


class Solution:
    def fractionAddition(self, expression: str) -> str:
        numerator, denominator = 0, 1
        i = 0
        while i < len(expression):
            sign = 1 if expression[i] != '-' else -1
            if expression[i] in '+-': i += 1
            num_start = i
            while expression[i] != '/': i += 1
            num = int(expression[num_start:i])
            i += 1
            den_start = i
            while i < len(expression) and expression[i].isdigit(): i += 1
            den = int(expression[den_start:i])
          
            numerator = numerator * den + sign * num * denominator
            denominator *= den
            
            g = gcd(abs(numerator), denominator)
            numerator //= g
            denominator //= g
        
        return f"{numerator}/{denominator}"
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