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# help algebra

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What is the positive solution to the equation x = 1/(2 + 1/(x + 2)) ?

Jun 28, 2021

#1
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Multiply the left side by x+2/x+2 to get, $$x=\frac{x+2}{2x+5}$$. Multiply both sides by 2x+5,

$$2x^2+5x= x + 2$$

Subtract x+2 on both sides

$$2x^2+4x-2= 0$$

Use the quadratic formula to find solutions of, $$x = -1 + \sqrt{2}, -1 - \sqrt{2}$$

We want the positive solution, which is $$-1 + \sqrt{2}$$

Jun 28, 2021
#2
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Positive solution: $$x = \sqrt{2}-1$$

Jun 28, 2021
edited by Guest  Jun 28, 2021