\(\frac{\sqrt{x}-5}{\sqrt{x}+5}=-1 \)
\(\Leftrightarrow\frac{(\sqrt{x}-5)\left(\sqrt{x}+5\right)}{(\sqrt{x}+5)\left(\sqrt{x}+5\right)}=-1\)
\(\Leftrightarrow\frac{x-25}{\left(\sqrt{x}+5\right)^2}=-1\)
\(\Leftrightarrow x-25=-\left(\sqrt{x}+5\right)^2\)
\(\Leftrightarrow x-25=-\left(x+10\sqrt{x}+25\right)\)
\(\Leftrightarrow x-25=-x-10\sqrt{x}-25\)
\(\Leftrightarrow 2x+10\sqrt{x}=0\)
\(\Leftrightarrow2\sqrt{x}\left(\sqrt{x}+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2\sqrt{x}=0\\\sqrt{x}+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}=-5\left(L\right)\end{matrix}\right.\Rightarrow x=0\)
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