Chapter 3 - Polynomial and Rational Functions - Summary Exercises on Solving Equations and Inequalities - Exercises - Page 382: 10

$x=2$

Step 1. Rewrite the equation as $3-\sqrt {x-1}=\sqrt {x+2}$ Step 2. Take square on both sides to get $9-6\sqrt {x-1}+x-1=x+2\longrightarrow 6\sqrt {x-1}=6$ Step 3. We can get the solutions $x-1=1^2$ and $x=2$ Step 4. Check the answer with the original equation, we find it fits.