we can do anything to an equation as long as we do it to both sides
given: [tex]\sqrt{3+\frac{(4+\sqrt{x+3})^2}{6}}=3[/tex]
square both sides
[tex]3+\frac{(4+\sqrt{x+3})^2}{6}=9[/tex]
minus 3 from both sides
[tex]\frac{(4+\sqrt{x+3})^2}{6}=6[/tex]
multiply both sides by 6
[tex](4+\sqrt{x+3})^2=36
square root both sides, remember to take the positive and negative roots
[tex]4+\sqrt{x+3}=+/-6[/tex]
minus 4
[tex]\sqrt{x+3}=-4+/-6[/tex]
square both sides
do for -4+6 and -4-6 (2 and -10)
[tex]x+3=4[/tex] and [tex]x+3=100[/tex]
minus 3
[tex]x=1[/tex] and [tex]x=97[/tex]
test for extraneous roots
x=97 doesn't work
the answer is x=1
