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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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Given,
`3f(x)+1=(3(x−1)​)/(x+1)+1=(4x−2)/(x-1)​`
`f(x)+3=(x−1)/(x+1)​+3=(4x−2)/(x-1)​`
Dividing we get
`(4x−2)/(4x+2)​=(2x−1)/(2x+1)​` `=f(2x)`
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