Question: Sketch the graph of the following rational function

(a) \(f\left( x \right)=\frac{2x}{{{x}^{2}}-4}\), with \(f''\left( x \right)=\frac{4x\left( 12+{{x}^{2}} \right)}{{{\left( {{x}^{2}}-4 \right)}^{3}}}\)

(b) \(f\left( x \right)=\frac{2x}{{{x}^{2}}+1}\), with \(f''\left( x \right)=\frac{4x\left( {{x}^{2}}-3 \right)}{{{\left( {{x}^{2}}+1 \right)}^{3}}}\)