\(\lim\limits_{t\rightarrow9}\dfrac{t-9}{\sqrt{t}-3}\)
\(=\lim\limits_{t\rightarrow9}\dfrac{\left(\sqrt{t}-3\right)\left(\sqrt{t}+3\right)}{\sqrt{t}-3}\)
\(=\lim\limits_{t\rightarrow9}\sqrt{t}+3=\sqrt{9}+3=3+3=6\)
\(\lim\limits_{x\rightarrow6}\dfrac{3x-18}{2x-12}\)
\(=\lim\limits_{x\rightarrow6}\dfrac{3\left(x-6\right)}{2\left(x-6\right)}=\lim\limits_{x\rightarrow6}\dfrac{3}{2}=\dfrac{3}{2}\)
\(\lim\limits_{t\rightarrow9}\dfrac{t-9}{\sqrt{t}-3}=\lim\limits_{t\rightarrow9}\dfrac{\left(t-9\right)\left(\sqrt{t}+3\right)}{t-9}=\lim\limits_{t\rightarrow9}\left(\sqrt{t}+3\right)=\sqrt{9}+3=6\)
\(\lim\limits_{x\rightarrow6}\dfrac{3x-18}{2x-12}=\lim\limits_{x\rightarrow6}\dfrac{3\left(x-6\right)}{2\left(x-6\right)}=\dfrac{3}{2}\)
