Question

Anyone??....Solve the equation & show work :) √2x + 3 - √x + 1 = 1

Answer 1

\[\sqrt{2x+3}-\sqrt{x+1}=1\quad,\quad x\geq -1\]\[\sqrt{2x+3}=1+\sqrt{x+1}\]\[2x+3=x+2+2\sqrt{x+1}\]\[x+1=2\sqrt{x+1}\]\[\sqrt{x+1}\left(\sqrt{x+1}-2\right)=0\]\[x=-1\quad\vee\quad x=3\]