$$ \begin{aligned} \frac{1}{a} &= \frac{1}{5950}+\frac{1}{5910}+\frac{1}{2920}&& \text{multiply ALL terms by } \color{blue}{ a\cdot5950\cdot5910\cdot2920 }. \\[1 em]a\cdot5950\cdot5910\cdot2920\cdot\frac{1}{a} &= a\cdot5950\cdot5910\cdot2920\cdot\frac{1}{5950}+a\cdot5950\cdot5910\cdot2920\cdot\frac{1}{5910}+a\cdot5950\cdot5910\cdot2920\cdot\frac{1}{2920}&& \text{cancel out the denominators} \\[1 em]102680340000 &= 17257200a+17374000a+35164500a&& \text{simplify right side} \\[1 em]102680340000 &= 17257200a+17374000a+35164500a&& \\[1 em]102680340000 &= 3a&& \text{ swap the left and right side of the equation } \\[1 em]3a &= 102680340000&& \text{ divide both sides by $ 3 $ } \\[1 em]a &= \frac{102680340000}{3}&& \\[1 em]a &= 34226780000&& \\[1 em] \end{aligned} $$

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