APFIVE Solving A Radical Equation With Substitution
Solve for x:
$$\sqrt{\frac{2*x+8}{x+2}} - \sqrt{\frac{x+2}{2*x+8}} = 1.$$
(Hint: Let $$u = \sqrt{\frac{2*x+8}{x+2}}$$ so that the equation simplifies to $$u - \frac{1}{u} = 1$$.)
A
$$x = \frac{2(5-\sqrt{5})}{\sqrt{5}-1}$$
B
$$x = \frac{5-\sqrt{5}}{\sqrt{5}-1}$$
C
$$x = \frac{2(5+\sqrt{5})}{\sqrt{5}+1}$$
D
$$x = \frac{2(\sqrt{5}-5)}{\sqrt{5}-1}$$
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