Answer
$7 \gt x$; where $x\ne 1$
OR
($7 \gt x \gt1$) U ($1\gt x)$
Work Step by Step
$$\frac{x + 5}{x - 1} \gt 2$$
First, we identify the vertical asymptotes by equaling the denominator to zero:
$$x - 1 \ne 0$$
$$x \ne 1$$
Then, we solve for $x$:
$(x + 5) \gt 2(x - 1)$
$x + 5 \gt 2x - 2$
$5 + 2 \gt 2x - x$
$7 \gt x$; where $x\ne 1$ and the domain can be expressed as:
Domain: {$x | (7 \gt x \gt1$) U ($1\gt x)$}.
