Answer
$(x+3)\sqrt[]{x-1}$
Work Step by Step
Simplifying each term and then combining like terms, the given expression, $
\sqrt[]{x^3-x^2}+\sqrt[]{9x-9}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{x^2(x-1)}+\sqrt[]{9(x-1)}
\\\\=
\sqrt[]{(x)^2\cdot(x-1)}+\sqrt[]{(3)^2\cdot(x-1)}
\\\\=
x\sqrt[]{x-1}+3\sqrt[]{x-1}
\\\\=
(x+3)\sqrt[]{x-1}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.