Answer
$37/4=y$
Work Step by Step
$\sqrt {y+3}-\sqrt{y-3}=1$
$\sqrt {y+3}-\sqrt{y-3}+\sqrt{y-3}=1+\sqrt{y-3}$
$\sqrt {y+3}=1+\sqrt{y-3}$
$(\sqrt {y+3})^2=(1+\sqrt{y-3})^2$
$(y+3)=(1+\sqrt{y-3})^2$
$y+3=1*1+(1*\sqrt{y-3})+(1*\sqrt{y-3})+(\sqrt{y-3})(\sqrt{y-3})$
$y+3=1+2\sqrt{y-3}+(y-3)$
$y+3=1+2\sqrt{y-3}+y-3$
$y+3=-2+2\sqrt{y-3}+y$
$3=-2+2\sqrt{y-3}$
$3+2=-2+2\sqrt{y-3}+2$
$5=2\sqrt{y-3}$
$5/2=2\sqrt{y-3}/2$
$5/2=\sqrt{y-3}$
$(5/2)^2=(\sqrt{y-3})^2$
$25/4=y-3$
$25/4+3=y-3+3$
$25/4+12/4=y$
$37/4=y$
$\sqrt {y+3}-\sqrt{y-3}=1$
$\sqrt {37/4+3}-\sqrt{37/4-3}=1$
$\sqrt {37/4+12/4}-\sqrt{37/4-12/4}=1$
$\sqrt {49/4}-\sqrt{25/4}=1$
$7/2-5/2=1$
$2/2=1$ (true)
