The solution set of 3xx+1+x+13x=2 , when x≠0 and x≠−1 is

[3xx+1]+[x+13x]=2⇒y+1y=2 where y=[3xx+1]⇒y2−2y+1=0⇒(y−1)2=0⇒y=1⇒[3xx+1]=1⇒3x=x+1⇒2x=1⇒x=12

The solution set of 3xx+1+x+13x=2 , when x≠0 and x≠−1 is

[3xx+1]+[x+13x]=2⇒y+1y=2 where y=[3xx+1]⇒y2−2y+1=0⇒(y−1)2=0⇒y=1⇒[3xx+1]=1⇒3x=x+1⇒2x=1⇒x=12

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The solution set of $\sqrt{\frac{3 x}{x + 1}} + \sqrt{\frac{x + 1}{3 x}} = 2$ , when $x \neq 0$ and $x \neq - 1$ is

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$\sqrt{[\frac{3 x}{x + 1}]} + \sqrt{[\frac{x + 1}{3 x}]} = 2 \Rightarrow y + \frac{1}{y} = 2$ where $y = \sqrt{[\frac{3 x}{x + 1}]}$

$\Rightarrow y^{2} - 2 y + 1 = 0 \Rightarrow {(y - 1)}^{2} = 0 \Rightarrow y = 1 \Rightarrow \sqrt{[\frac{3 x}{x + 1}]} = 1 \Rightarrow 3 x = x + 1 \Rightarrow 2 x = 1 \Rightarrow x = \frac{1}{2}$

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The solution set of 3xx+1+x+13x=2 , when x≠0 and x≠−1 is

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The solution set of $\sqrt{\frac{3 x}{x + 1}} + \sqrt{\frac{x + 1}{3 x}} = 2$ , when $x \neq 0$ and $x \neq - 1$ is