Simplify the complex fraction:
x
2
−
4
x
+
3
x
2
+
6
x
+
8
x
−
3
x
+
2
\displaystyle \frac{{\frac{{{x}^{{2}}-{4}{x}+{3}}}{{{x}^{{2}}+{6}{x}+{8}}}}}{{\frac{{{x}-{3}}}{{{x}+{2}}}}}
x
+
2
x
−
3
x
2
+
6
x
+
8
x
2
−
4
x
+
3
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