Perform the operation and simplify:
x
−
4
x
+
5
÷
x
2
−
6
x
+
8
x
−
2
\displaystyle \frac{{{x}-{4}}}{{{x}+{5}}}\div\frac{{{x}^{{2}}-{6}{x}+{8}}}{{{x}-{2}}}
x
+
5
x
−
4
÷
x
−
2
x
2
−
6
x
+
8
1
x
−
1
\displaystyle \frac{{1}}{{{x}-{1}}}
x
−
1
1
1
x
+
5
\displaystyle \frac{{1}}{{{x}+{5}}}
x
+
5
1
1
x
−
4
\displaystyle \frac{{1}}{{{x}-{4}}}
x
−
4
1
1
x
−
2
\displaystyle \frac{{1}}{{{x}-{2}}}
x
−
2
1
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