Simplify: 2/(√5+√3) + 1/ (√3+√2) + 3/ (√5+√2)

asked by guest
on Oct 06, 2024 at 11:20 pm



You asked:

Simplify the expression: \(\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{3}{\sqrt{5} + \sqrt{2}}\)

MathBot Answer:

Simplified:

\[ \frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{3}{\sqrt{5} + \sqrt{2}} = \frac{6 \left(\sqrt{6} + 3 + \sqrt{10} + \sqrt{15}\right)}{2 \sqrt{30} + 5 \sqrt{5} + 8 \sqrt{2} + 7 \sqrt{3}} \]

Factored:

\[ \frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{3}{\sqrt{5} + \sqrt{2}} = \frac{6 \left(\sqrt{6} + 3 + \sqrt{10} + \sqrt{15}\right)}{\left(\sqrt{2} + \sqrt{3}\right) \left(\sqrt{2} + \sqrt{5}\right) \left(\sqrt{3} + \sqrt{5}\right)} \]


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