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Let $f$ and $g$ be functions defined by $f(x)=\frac{x}{x+1}, g(x)=\frac{x}{1-x}$, then $(f \circ g)(x)$ is
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$x$
$(f \circ g)(x)=f(g(x))=f\left(\frac{x}{1-x}\right)=\frac{\frac{x}{1-x}}{\frac{x}{1-x}+1}=\frac{x}{x+1-x}=x$
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