Answer
$\color{blue}{(-\infty, -\frac{1}{2}) \cup (-\frac{1}{2}, 1) \cup (1, +\infty)}$
Work Step by Step
The denominator of a rational expression is not allowed to be equal to zero as it will make the expression undefined.
Find the values of $x$ for which the denominator is equal to zero by equating the denominator to zero:
$(4x+2)(x-1)= 0$
Use the Zero-Product Property by equating each factor to zero then solving each equation to obtain:
\begin{array}{ccc}
&4x+2 = 0 &\text{ or } &x-1=0
\\&4x=-2 &\text{or} &x=1
\\&x=-\frac{1}{2} &\text{or} &x=1
\end{array}
This means that the value of $x$ can be any real number except $-\frac{1}{2}$ and $1$.
Therefore, the domain of the given rational expression is the set of real numbers except $-\frac{1}{2}$ and $1$.
In interval notation, the domain is:
$\color{blue}{(-\infty, -\frac{1}{2}) \cup (-\frac{1}{2}, 1) \cup (1, +\infty)}$
