Math Help: Algebra

Second one is along the same lines.

divide by 2 gets you
1 = sqrt(x-3) - sqrt(2x-4)

rearrange
1 - sqrt(x-3) = -sqrt(2x-4)

change sign
sqrt(x-3) - 1 = sqrt(2x-4)

square both sides
x - 3 - 2sqrt(x-3) + 1 = 2x - 4

rearrange
x - 2sqrt(x-2) - 2 = 2x - 4

then rearrange again
-x + 2 = 2sqrt(x-2)

square
x^2 - 4x + 4 = 4x - 8

rearrange
x^2 = -12

try to solve it and you're sqrting a negative, then you blow up the world. There is no solution.