College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises - Page 76: 114



Work Step by Step

Multiplying by the conjugate of the denominator, the rationalized-denominator from of the given expression, $ \dfrac{2}{7-\sqrt{3}} ,$ is \begin{array}{l}\require{cancel} \dfrac{2}{7-\sqrt{3}}\cdot\dfrac{7+\sqrt{3}}{7+\sqrt{3}} \\\\= \dfrac{2(7+\sqrt{3})}{(7)^2-(\sqrt{3})^2} \\\\= \dfrac{2(7+\sqrt{3})}{49-3} \\\\= \dfrac{2(7+\sqrt{3})}{46} \\\\= \dfrac{\cancel{2}(7+\sqrt{3})}{\cancel{2}(23)} \\\\= \dfrac{7+\sqrt{3}}{23} .\end{array}
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