$($a$)$ What is wrong with the following equation?

$\frac{x^{2}x-42}{x-6}=x7$

$(x-6)(x7)x^{2}x-42$

The left$-$hand side is not defined for $x=0,$ but the right$-$hand side is$.$

The left$-$hand side is not defined for $x-6,$ but the right$-$hand side is$.$

None of these $-$ the equation is correct.

$($b$)$ In view of part $($a$),$ explain why the following equation is correct.

$\underset{x6}{lim}\frac{x^{2}x-42}{x-6}=\underset{x6}{lim}(x7)$

Since $\frac{x^{2}x-42}{x-6}$ and $x7$ are both continuous, the equation follows.

Since the equation holds for all $x=6,$ it follows that both sides of the equation approa

This equation follows from the fact that the equation in part $($a$)$ is correct.

None of these $-$ the equation is not correct.