# Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 617: 42

x = $\frac{ 2 \sqrt 15 + \sqrt 45}{30}$

#### Work Step by Step

$\frac{4\sqrt 15}{1 + \sqrt 3}$ = $\frac{1 + \sqrt 3}{x}$ We cross multiply $4 \sqrt 15 (x) = (1 + \sqrt 3)(1 + \sqrt 3)$ We divide both sides by $4 \sqrt 15$ x = $\frac{1 + 2 \sqrt 3 + 3}{4 \sqrt 15}$ We add 3 and 1 together x = $\frac{2 \sqrt 3 + 4}{4 \sqrt 15}$ We divide the coefficients by 2 x = $\frac{ \sqrt 3 + 2}{2 \sqrt 15}$ We multiply it by the conjugate which is $\sqrt 15$ x = $\frac{ \sqrt 3 + 2}{2 \sqrt 15} \times \frac{\sqrt 15}{\sqrt 15}$ We multiply the numerator and denominator to simplify x = $\frac{ \sqrt 3 + 2 \times \sqrt 15}{2 \sqrt 15 \times \sqrt 15}$ x = $\frac{ 2 \sqrt 15 + \sqrt 45}{30}$

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