Answer
$181/36=x$
Work Step by Step
$\sqrt{x+3} + \sqrt {x-5} = 3$
$\sqrt{x+3} + \sqrt {x-5}-\sqrt {x-5} = 3-\sqrt {x-5}$
$\sqrt{x+3} = 3-\sqrt {x-5}$
$(\sqrt{x+3})^2= (3-\sqrt {x-5})^2$
$x+3 = 3*3+3*(-\sqrt {x-5})+(-\sqrt {x-5})*3+(-\sqrt {x-5})(-\sqrt {x-5})$
$x+3 = 9-6\sqrt {x-5}+(x-5)$
$x+3= 9-6\sqrt {x-5}+x-5$
$3 = 4-6\sqrt {x-5}$
$-1 = -6\sqrt {x-5}$
$(-1)^2 = (-6\sqrt {x-5})^2$
$1 = 36(x-5)$
$1/36 = 36(x-5)/36$
$1/36=x-5$
$1/36+5=x-5+5$
$181/36=x$
$\sqrt{x+3} + \sqrt {x-5} = 3$
$\sqrt{181/36+3} + \sqrt {181/36-5} = 3$
$\sqrt{181/36+3} + \sqrt {1/36} = 3$
$\sqrt{181/36+108/36} + \sqrt {1/36} = 3$
$\sqrt{289/36} + \sqrt {1/36} = 3$
$17/6 +1/6 = 3$
$18/6=3$ (true)
