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\frac{\sqrt{5}-3}{2}+\frac{2}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.
\frac{\sqrt{5}-3+2}{2}
Since \frac{\sqrt{5}-3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.
\frac{\sqrt{5}-1}{2}
Do the calculations in \sqrt{5}-3+2.