(a) what is wrong with the following equation?

x2 + x − 42/ x − 6 = x + 7

1)(x − 6)(x + 7) ≠ x2 + x − 42
2)the left-hand side is not defined for x = 0, but the right-hand side is.
3)the left-hand side is not defined for x = 6, but the right-hand side is.
4)none of these — the equation is correct.

so.. the left-hand-side does indeed simplify to x+7, so the equation does check out.

however, notice something, for the equation of x+7, when x = 6, we get (6) + 7 which is 13.

BUT for the rational, we get    

so, even though the siimplification is correct, the rational or original expression is constrained in its domain.