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If f(x)=(3x-2)/(2x-3), prove that f(f(x)...

If `f(x)=(3x-2)/(2x-3),` prove that `f(f(x)))=x` for all `x in R-{3/2}` .

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`f(x) =\frac{3 x-2}{2 x-3} `
`f(f(x)) =\frac{3 f(x)-2}{2 f(x)-3} `
`=\frac{3\left(\frac{3 x-2}{2 x-3}\right)-2}{2\left(\frac{3 x-2}{2 x-3}\right)-3} `
`=\frac{9 x-6-4 x+6}{6 x-4-6 x+9} `
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