Inter. Algebra

I find it curious here:
a - b=2 in this case,

rationalize by multplying both sides by a+b, getting
a-b=2
a^2-b^2=2(a+b)
2x+3-x+2=2(a+b)
(x+5)/2 = a+b
now add the original equation..
2= a-b
or 2a= 2+ x/2 + 5/2
4sqrt(2x+3)= x+9
square both sides..
16(2x+3)= x^2+18x + 81
x^2-14x+33=0
(x-3)(x-11)=0

square root sign 2x+3 - square root sign x-2 = 2. And the instructions are to solve the equation.

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