sqrt [(5) / (x + 3)] = 4 / [x + sqrt(4)]
sqrt [ (5) / (x + 3)] = 4/ [x + 2] square both sides
5 / [x + 3] = 16/ [x^2 + 4x + 4] cross-multiply
5 [ x^2 + 4x + 4 ] = 16[x + 3] simplify
5x^2 + 20x + 20 = 16x + 48
5x^2 + 4x -28 = 0 factor
[5x + 14] [ x - 2] = 0
Setting each factor to O we have that x = -14/5 or x = 2
However.....x = -14/5 produces a negative quantity on the right hand side of the original equation, and we can never get a negative out of the left hand side......so.......the two sides would have unequal signs, so x = -14/5 is not a soluition
So.......x = 2 is the only solution.....
