Rational functions/Composition/2x^2-4x+3 divided by x-2 and x+1 divided by x^2-4/Exercise

Compute the compositions ${}f\circ g$ and ${}g\circ f$ for the rational functions

$f(x)={\frac {2x^{2}-4x+3}{x-2}}\,\,{\text{ and }}\,\,g(x)={\frac {x+1}{x^{2}-4}}.$

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