Question

# Determine the domains of the given rational functions. 4/((x^3)+(x^2))

Rational functions
Determine the domains of the given rational functions.
$$\displaystyle\frac{{4}}{{{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}}}$$

By rule of the domain of the function that denominator can not be zero, we have $$\displaystyle{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}≠{0}$$
$$\displaystyle{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}={\left({x}^{{2}}\right)}{\left({x}+{1}\right)},$$ that is xero for $$\displaystyle{x}^{{2}}={0}$$, viz $$x=0$$ and $$x+1=0, viz\ x=-1$$.
So, we conclude, the domain of the given function is $$\displaystyle{R}{\left\lbrace{\left(-{1.0}\right\rbrace}\right.}$$