Question

Determine o valor de X:

$1 + \frac{1}{\frac{1}{2} +\frac{1}{\frac{1}{2} + \frac{1}{x}}} = 2$
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Answer 1

$1+\frac{1}{\frac{1}{2}+\frac{1}{\frac{1}{2}+\frac{1}{x} } }=2$

$\frac{1}{\frac{1}{2}+\frac{1}{\frac{1}{2}+\frac{1}{x} } }=2-1$

$\frac{1}{\frac{1}{2}+\frac{1}{\frac{1}{2}+\frac{1}{x} } }=1$

$1=\frac{1}{2}+\frac{1}{\frac{1}{2}+\frac{1}{x} }$

$1=\frac{1}{2}+\frac{1}{\frac{x}{2x}+\frac{2}{2x} }$

$1=\frac{1}{2}+\frac{1}{\frac{x+2}{2x} }$

$1=\frac{1}{2}+\frac{2x}{x+2}$

$1-\frac{1}{2} =\frac{2x}{x+2}$

$\frac{2}{2}-\frac{1}{2}= \frac{2x}{x+2}$

$\frac{1}{2}= \frac{2x}{x+2}$

$x+2=2\cdot 2x$

$x+2=4x$

$x-4x=-2$

$-3x=-2$

$3x=2$

$x=\frac{2}{3}$