Question

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Answer 1

\(a,\Leftrightarrow\sqrt{x+1}-1=\sqrt{x-1}\left(x\ge1\right)\\ \Leftrightarrow x+2-2\sqrt{x+1}=x-1\\ \Leftrightarrow2\sqrt{x+1}=3\\ \Leftrightarrow\sqrt{x+1}=\dfrac{3}{2}\Leftrightarrow x+1=\dfrac{9}{4}\\ \Leftrightarrow x=\dfrac{5}{4}\left(tm\right)\\ b,\Leftrightarrow\sqrt{2x+2}=1-\sqrt{2x+3}\left(x\ge-1\right)\\ \Leftrightarrow2x+2=2x+4-2\sqrt{2x+3}\\ \Leftrightarrow2\sqrt{2x+3}=2\\ \Leftrightarrow\sqrt{2x+3}=1\\ \Leftrightarrow2x+3=1\\ \Leftrightarrow x=-1\left(tm\right)\)