Solving A Radical Equation With Substitution

Question

Solve the following equation for x:

$$\sqrt{\frac{2*x+8}{x+2}} - \sqrt{\frac{x+2}{2*x+8}} = 1.$$

(Hint: Using the substitution $$u = \sqrt{\frac{2*x+8}{x+2}}$$, the equation becomes $$u - \frac{1}{u} = 1$$.)

Accepted Answer

$$x = \frac{2(5-\sqrt{5})}{\sqrt{5}-1}$$

Answer

$$x = \frac{2(\sqrt{5}-5)}{\sqrt{5}-1}$$

Answer

$$x = \frac{5-\sqrt{5}}{\sqrt{5}-1}$$

Answer

$$x = \frac{2(5+\sqrt{5})}{\sqrt{5}+1}$$

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