Question

Determine the domains of the given rational functions. (x^2-9)/(x^3-x)

Rational functions
ANSWERED
asked 2021-06-20
Determine the domains of the given rational functions.
\(\displaystyle\frac{{{x}^{{2}}-{9}}}{{{x}^{{3}}-{x}}}\)

Answers (1)

2021-06-21

By rules of the domain ofthe function that denominator can not be zero, we have
\(\displaystyle{x}^{{3}}-{x}\frac{=}{{0}}\)
\(\displaystyle{x}^{{3}}-{x}\) can be written as \(\displaystyle{x}^{{3}}-{x}={x}{\left({x}^{{2}}-{1}\right)}\)
From here we have that
\(\displaystyle{x}^{{3}}—{x}={x}{\left({x}^{{2}}-{1}\right)}={0}\) when \(x = 0\) or \(\displaystyle{x}^{{2}}—{1}={0}\).
\(\displaystyle{x}^{{2}}—{1}={0}\) is quadratic function and we have
\(\displaystyle{x}^{{2}}={1}\)
Then domain of the given function is
\(R\{-1,0,1\}\)

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