+) TH1: $m=n$Chia $x^n:$
$f(x)=\frac{\frac{a_nx^n}{x^n}+\frac{a_{n-1}x^{n-1}}{x^n}+......+\frac{a_1x}{x^n}+\frac{a_0}{x^n}}{\frac{b_nx^n}{x^n}+........................+\frac{b_0}{x^n}}$
$=> \mathop {\lim }\limits_{x \to +\infty }f(x)=\mathop {\lim }\limits_{x \to +\infty }\frac{an}{bn}=\frac{a}{b}.$
+) TH2: $m>n$
Chia $x^m:$
$f(x)=\frac{\frac{a_nx^n}{x^m}+.................+\frac{a_0}{x^m}}{\frac{b_mx^m}{x^m}+..............\frac{b_0}{x^m}}$
$=>\mathop {\lim }\limits_{x \to +\infty }f(x)=\mathop {\lim }\limits_{x \to +\infty }\frac{0}{b_m}=0$
+) TH3: $m<n$ không có đường tiệm cận $=>\varnothing $
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TQ:
$\mathop {\lim }\limits_{x \to \pm \infty }f(x)=\frac{an}{bm}.\mathop {\lim }\limits_{x \to \pm \infty }x^{n-m}$
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3TF, mãi mãi một tình yêu <3