Simplify the expression of the following rational functions.
g\left(x\right)=\dfrac{x-3}{x^2-9}
g\left(x\right)=\dfrac{x^2-1}{\left(x+1\right)^2}
g\left(x\right)=\dfrac{x^2-4x+4}{x^2-4}
g\left(x\right)=\dfrac{x-1}{x^3-x}
g\left(x\right)=\dfrac{x^4-x^3}{x^5-x^4}
g\left(x\right)=\dfrac{x^5-x^3}{x^3\left(x-1\right)^2}
g\left(x\right)=\dfrac{x^3-1}{x^2-1}