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If f is a real function defined by `f(x)=(x-1)/(x+1)`, then prove that `f(2x)=(3f(x)+1)/(f(x)+3)`

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`f(x)=(x-1)/(x+1)`
`f(2x)=(2x-1)/(2x+1)-(1)`
`f(2x)=(3f(x)+1)/(f(x)+3)`
RHS
`(3((x-1)/(x+1))+1)/((x-1)/(x+1)+3)`
`(3(x-1)+x+1)/(x-1)+3(x+1)`
`(3x-3+x+1)/(x-1+3x+3)`
`(4x-2)/(4x+2)`
...
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