Notice that
so on the left side, a factor of <em>x</em> - 7 in the numerator and denominator can cancel
But we can only cancel them out as long as <em>x</em> ≠ 7 (because otherwise we'd have the indeterminate form 0/0 on the left side).
So, the equation is true for all <em>x</em> <u>except</u> <em>x</em> = 7. In set notation,
In interval notation,