Answer
$x=3/16$
Work Step by Step
$\sqrt {3x+1} + \sqrt {3x} =2$
$\sqrt {3x+1} + \sqrt {3x}-\sqrt {3x} =2-\sqrt {3x}$
$\sqrt {3x+1} =2- \sqrt {3x}$
$(\sqrt {3x+1})^2 =(2- \sqrt {3x})^2$
$3x+1 = 2*2+2*(-\sqrt {3x})+(-\sqrt {3x}*2)+(-\sqrt{3x})*(-\sqrt {3x})$
$3x+1 = 4-2\sqrt {3x}-2\sqrt {3x}+(\sqrt{3x*3x})$
$3x+1 = 4-4\sqrt {3x}+3x$
$1 = 4-4\sqrt {3x}$
$1-1+4\sqrt{3x} = 4-4\sqrt {3x}-1+4\sqrt{3x}$
$4\sqrt{3x} = 4-1$
$4\sqrt{3x} = 3$
$4\sqrt{3x}/4 = 3/4$
$\sqrt{3x} = 3/4$
$(\sqrt{3x})^2 = (3/4)^2$
$3x=9/16$
$3x*16=9/16*16$
$3x*16=9$
$3x*16/3=9/3$
$x*16=3$
$16x=3$
$16x/16=3/16$
$x=3/16$
$\sqrt {3x+1} + \sqrt {3x} =2$
$\sqrt {3*\frac{3}{16}+1} + \sqrt {3*\frac{3}{16}} =2$
$\sqrt {\frac{9}{16}+1} + \sqrt {\frac{9}{16}} =2$
$\sqrt {\frac{25}{16}} + \frac{\sqrt 9}{\sqrt {16}} =2$
$\frac{\sqrt {25}}{\sqrt {16}} + \frac{\sqrt 9}{\sqrt {16}} =2$
$\frac{5}{4} + \frac{3}{4} =2$
$\frac{8}{4}=2$
$2=2$ (true)
