Answer
$x=-1,3$
Work Step by Step
$\sqrt {2x+3}-\sqrt {x+1}=1$
$\sqrt {2x+3}=\sqrt {x+1}+1$
$2x+3=x+1+2\sqrt {x+1}+1$
$x+1=2\sqrt {x+1}$
$x^2+2x+1=4x+4$
$x^2-2x-3=0$
$(x-3)(x+1)=0$
$x=-1,3$
Check, both fit.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.8 Solving Equations - A.8 Assess Your Understanding - Page A70: 55
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