Question 71909
1. I need to figure out the solution set for radical(3x+7)+ radical(x+6)=3. 
{{{sqrt(3x+7) + sqrt(x+6)}}} = 3
:
Subtract {{{sqrt(x+6)}}} from both sides:
{{{sqrt(3x+7)}}} = 3 -{{{sqrt(x+6)}}}
:
Square both sides; FOIL (3-Sqrt(x+6))*(3-Sqrt(x+6):
3x + 7 = 9 - {{{6sqrt(x-6)}}} + (x+6)
:
3x + 7 = 9 - {{{6sqrt(x-6)}}} + x + 6
:
3x + 7 = 9 + 6 + x -{{{6sqrt(x+6)}}}
:
3x + 7 = 15 + x -{{{6sqrt(x+6)}}}
:
Get the radical on the right by itself:
3x - x + 7 - 15 =  -{{{6sqrt(x+6)}}}
:
2x - 8 = -{{{6sqrt(x+6)}}}
:
Square both sides; FOIL (2x - 8)^2
4x^2 - 32x + 64 = +36(x+6)
4x^2 - 32x + 64 = 36x + 216
4x^2 - 32x - 36x + 64 - 216 = 0
4x^2 - 68x - 152 = 0
:
Simplify, divide equation by 4:
x^2 - 17x - 38 = 0
:
Factors to:
(x - 19)(x + 2) = 0
:
x = +19 and x = -2; only the x = -2 is a solution, check it for yourself 
:
:
2. Find the domain of: x-2/radical(x+2)
{{{(x-2)/sqrt(x+2)}}}
There are two no-no's to remember. You can't have 0 in the denominator and 
you can have a negative result inside the radical: domain of:  x > -2