Answer
$\dfrac{8-6\sqrt{x}+x}{8-2x}$
Work Step by Step
Multiplying both the numerator and the denominator by the conjugate of the denominator, the rationalized-denominator form of the given expression, $
\dfrac{4-\sqrt{x}}{4+2\sqrt{x}}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{4-\sqrt{x}}{4+2\sqrt{x}}\cdot\dfrac{4-2\sqrt{x}}{4-2\sqrt{x}}
\\\\=
\dfrac{4(4)+4(-2\sqrt{x})-\sqrt{x}(4)-\sqrt{x}(-2\sqrt{x})}{(4)^2-(2\sqrt{x})^2}
\\\\=
\dfrac{16-8\sqrt{x}-4\sqrt{x}+2x}{16-4x}
\\\\=
\dfrac{16-12\sqrt{x}+2x}{16-4x}
\\\\=
\dfrac{2(8-6\sqrt{x}+x)}{2(8-2x)}
\\\\=
\dfrac{\cancel{2}(8-6\sqrt{x}+x)}{\cancel{2}(8-2x)}
\\\\=
\dfrac{8-6\sqrt{x}+x}{8-2x}
.\end{array}
Note that the value of the variable is assumed to be positive.
