Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-3 Binomial Radical Expressions - Practice and Problem-Solving Exercises - Page 379: 49

Answer

$2$

Work Step by Step

Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression, $ \left( \sqrt{a+1}+\sqrt{a-1} \right)\left( \sqrt{a+1}-\sqrt{a-1} \right) ,$ is equivalent to \begin{align*} & \left( \sqrt{a+1} \right)^2-\left(\sqrt{a-1} \right)^2 \\&= a+1-(a-1) \\&= a+1-a+1 \\&= 2 .\end{align*} Hence, the simplified form of the given expression is $ 2 $.
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