Perform the operation and simplify:
x
+
4
x
2
+
7
x
+
12
÷
x
−
5
x
+
3
\displaystyle \frac{{{x}+{4}}}{{{x}^{{2}}+{7}{x}+{12}}}\div\frac{{{x}-{5}}}{{{x}+{3}}}
x
2
+
7
x
+
12
x
+
4
÷
x
+
3
x
−
5
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