Question 77195
sqrt (6x+7)  -  sqrt (3x+3)  = 1

Square it the way it is so you end up with just one new radical:

Result of square both sides is:
6x+7 -2sqrt[(6x+7)(3x+3)] + 3x+3 = 1

Isolate the remaining radical:

9x+10 - 2[....] = 1
2[....]= 9x+9
Square to get rid of the radical:
-----
4[(6x+7)(3x+3) = [9(x+1)]^2
Now, solve for x.
I'll leave that to you.
Cheers,
Stan H.