#### Answer

$(2-x)\sqrt[]{x-1}$

#### Work Step by Step

Simplifying each term and then combining like terms, the given expression, $
\sqrt[]{4x-4}-\sqrt[]{x^3-x^2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{4(x-1)}-\sqrt[]{x^2(x-1)}
\\\\=
\sqrt[]{(2)^2\cdot(x-1)}-\sqrt[]{(x)^2\cdot(x-1)}
\\\\=
2\sqrt[]{x-1}-x\sqrt[]{x-1}
\\\\=
(2-x)\sqrt[]{x-1}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.