If \(1+\cfrac{5x}{1-\cfrac{1}{2+\cfrac{2x}{1-x}}}=3\), then the value of 'x' is:
Simplifying the innermost part, \(2+\frac{2x}{1-x}=\frac{2}{1-x}\), so \(1-\frac{1}{2/(1-x)}=1-\frac{1-x}{2}=\frac{1+x}{2}\). The equation becomes \(1+\frac{10x}{1+x}=3\), giving \(10x=2(1+x)\), so \(8x=2\) and \(x=\frac{1}{4}\).
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