Solución

lim⁡t→9t−9t−3=9−93−3=00\mathop {\lim }\limits_{t \to 9} {{t - 9} \over {\sqrt t - 3}} = {{9 - 9} \over {3 - 3}} = {0 \over 0}

Así, lim⁡t→9t−9t−3=lim⁡t→9(t−9)(t+3)(t−3)(t+3)=lim⁡t→9(t+3)=6\mathop {\lim }\limits_{t \to 9} {{t - 9} \over {\sqrt t - 3}} = \mathop {\lim }\limits_{t \to 9} {{\left( {t - 9} \right)\left( {\sqrt t + 3} \right)} \over {\left( {\sqrt t - 3} \right)\left( {\sqrt t + 3} \right)}} = \mathop {\lim }\limits_{t \to 9} \left( {\sqrt t + 3} \right) = 6