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When the numerator of any expression or fraction is zero then the result is zero because zero divided by any number is always equal to zero.
That is correct.
When the denominator is equal to zero, the expression is undefined. Close to those places, the expression tends towards plus infinity, or minus infinity. In other words, setting the denominator to zero will tell you where there are vertical asymptotes.
A zero. Zero in the denominator make the expression undefined for algebraic purposes.
You must look at the condition when the expression is greater or equal to zero and the case (condition) when it is less that zero.