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(x-6)$\sqrt[2]{x+1}$ +(x-15)$\sqrt[2]{x-2}$ +18 =0
\[\begin{array}{l}
(x - 6)\sqrt {x + 1} + (x - 15)\sqrt {x - 2} + 18 = 0\\
\Leftrightarrow (x - 6)(\sqrt {x + 1} + \sqrt {x - 2} ) - 9(\sqrt {x - 2} - 2) = 0\\
\Leftrightarrow (x - 6)(\sqrt {x + 1} + \sqrt {x - 2} ) - 9(\frac{{x - 6}}{{\sqrt {x - 2} + 2}}) = 0\\
\Leftrightarrow (x - 6)\left( {\sqrt {x + 1} + \sqrt {x - 2} - \frac{9}{{\sqrt {x - 2} + 2}}} \right) = 0
\end{array}\]
 
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