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Chapter 4: Problem 129

Find \(\frac{x}{y}\) for \(x=-\frac{1}{2}\) and \(y=\frac{\sqrt{3}}{2},\) and then rationalize the denominator.

Short Answer

Expert verified
\(-\sqrt{3}/3\)

Step by step solution

01

Substitute \(x\) and \(y\)

Substitute \(x=-\frac{1}{2}\) and \(y=\frac{\sqrt{3}}{2}\) into the expression \(\frac{x}{y}\) we get \(\frac{-1/2}{\sqrt{3}/2}\)
02

Simplify the expression

The value can be simplified as \(\frac{-1}{\sqrt{3}}\) by cancelling the common factor of \(1/2\) from the numerator and the denominator.
03

Rationalize the denominator

To rationalize the denominator, multiply both the numerator and denominator by \(\sqrt{3}\); this gives \(\frac{-1\cdot \sqrt{3}}{\sqrt{3}\cdot \sqrt{3}}\), which simplifies to \(\frac{-\sqrt{3}}{3}\).

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