\(y=\dfrac{x-3}{x-1}\)
=>\(y'=\dfrac{\left(x-3\right)'\left(x-1\right)-\left(x-3\right)\left(x-1\right)'}{\left(x-1\right)^2}\)
=>\(y'=\dfrac{\left(x-1\right)-\left(x-3\right)}{\left(x-1\right)^2}=\dfrac{2}{\left(x-1\right)^2}\)
\(y'\left(2\right)=\dfrac{2}{\left(2-1\right)^2}=2\)
\(y\left(2\right)=\dfrac{2-3}{2-1}=\dfrac{-1}{1}=-1\)
Phương trình tiếp tuyến là:
y-y(2)=y'(2)(x-2)
=>y-(-1)=2(x-2)=2x-4
=>y+1=2x-4
=>y=2x-4-1=2x-5
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