Answer
The answer is: $x=(\sqrt7-1)\div4$.
Work Step by Step
Given:
$x/(2+\sqrt7)=(3-\sqrt7)/4$
By cross multiplication we get,
$4*x=(3-\sqrt7)*(2+\sqrt7)$
$4x=(3*2+3\sqrt7-2\sqrt7-\sqrt7^{2})$
$4x=(6+\sqrt7-7)$
$x=(\sqrt7-1)\div4$
Algebra 1: Common Core (15th Edition)
by Charles, Randall I.
Published by
Prentice Hall
ISBN 10:
0133281140
ISBN 13:
978-0-13328-114-9
Chapter 10 - Radical Expressions and Equations - 10-3 Operations With Radical Expressions - Practice and Problem-Solving Exercises - Page 630: 41
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