Sixes And Sevens

$\begin{aligned} \dfrac{7\left(6 - \dfrac{1}{7}\right)}{6\left(7 - \dfrac{1}{6}\right)} & = {\dfrac{\cancel{7}×\dfrac{\cancel{41}}{\cancel{7}}}{\cancel{6} × \dfrac{\cancel{41}}{\cancel{6}}}}\\ \\ & = \color{#3D99F6}{\boxed{1}} \end{aligned}$

$\frac{7(6-\frac{1}{7})}{6(7-\frac{1}{6})}$

First simplify by distributing into the brackets.

$\frac{42-1}{42-1}$

Realize the numerator is non zero and equal to the denominator.

$\boxed{1}$