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Chapter 5: Problem 73

Perform the indicated operations. Simplify the answer when possible. \(\frac{\sqrt{2}}{\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}}\)

Short Answer

Expert verified
The result of this operation is \(\frac{5\sqrt{6}}{6}\).

Step by step solution

01

Simplifying the first fraction

Multiply numerator and denominator of the first fraction by \(\sqrt{3}\). This results in \(\frac{\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}} = \frac{\sqrt{6}}{3}\).
02

Simplifying the second fraction

Multiply numerator and denominator of the second fraction by \(\sqrt{2}\). This results in \(\frac{\sqrt{3}*\sqrt{2}}{\sqrt{2}*\sqrt{2}} = \frac{\sqrt{6}}{2}\).
03

Adding the simplified fractions

Add the two simplified fractions \(\frac{\sqrt{6}}{3}\) and \(\frac{\sqrt{6}}{2}\). As the numerators are the same, add the fractions by finding a common denominator, which is 6 in this case. The result is \(\frac{2\sqrt{6}}{6} + \frac{3\sqrt{6}}{6} = \frac{5\sqrt{6}}{6}\).

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Most popular questions from this chapter

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