\[\begin{alignat*}{3}\mathop {\lim }\limits_{w \to 3} \frac{{{w^2} - 8w}}{{4 - 7w}} & = \frac{{\mathop {\lim }\limits_{w \to 3} \left( {{w^2} - 8w} \right)}}{{\mathop {\lim }\limits_{w \to 3} \left( {4 - 7w} \right)}} & & \hspace{0.25in}{\mbox{Property 4}}\\ & = \frac{{\mathop {\lim }\limits_{w \to 3} {w^2} - \mathop {\lim }\limits_{w \to 3} 8w}}{{\mathop {\lim }\limits_{w \to 3} 4 - \mathop {\lim }\limits_{w \to 3} 7w}} & & \hspace{0.25in}{\mbox{Property 2}}\\ & = \frac{{\mathop {\lim }\limits_{w \to 3} {w^2} - 8\mathop {\lim }\limits_{w \to 3} w}}{{\mathop {\lim }\limits_{w \to 3} 4 - 7\mathop {\lim }\limits_{w \to 3} w}} & & \hspace{0.25in}{\mbox{Property 1}}\\ & = \frac{{{3^2} - 8\left( 3 \right)}}{{4 - 7\left( 3 \right)}} & & \hspace{0.25in}{\mbox{Properties 7, 8, \& 9}}\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{15}}{{17}}}} & & & \end{alignat*}\]

E'tibor bering, biz birinchi bosqichda 4-xususiyatdan foydalana oldik, chunki maxrajdagi chegarani baholaganimizdan so'ng biz uning nolga teng emasligini aniqladik.