Question

Rationalize the denominator. $$ \frac{5}{\sqrt{3}-1} $$

   Rationalize the denominator.
$$
\frac{5}{\sqrt{3}-1}
$$

Algebra and Trigonometry

Algebra and Trigonometry

Robert Blitzer 6th Edition

Chapter 0, Problem 52

Instant Answer

Solved by Expert Cory Kuzinski

06/03/2020

Step 1

This gives us: $$ \frac{5}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1} $$ Show more…

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Rationalize the denominator. $$ \frac{5}{\sqrt{3}-1} $$

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Key Concepts

Rationalizing the Denominator

Rationalizing the denominator is a technique used in algebra to eliminate irrational numbers, such as square roots, from the denominator of a fraction. This process is performed by multiplying the numerator and the denominator by an appropriate expression that will result in a rational denominator, thereby simplifying the expression for further computation or comparison.

Conjugate

When the denominator of a fraction is a binomial containing radical terms, the conjugate of that binomial (which has the same terms but the opposite sign between them) is used to rationalize the denominator. Multiplying the original expression by a fraction equivalent to 1 that has the conjugate in both the numerator and denominator leverages the difference of squares formula to produce a rational denominator.

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