Expert: Scott A Wilson - 9/24/2009

Question
I am having a hard time understanding why the denominator or numberator being 0 would be a restriction in solving an equation.  What if x is 0?

Answer
numerator=0, denominator<>0
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If the problem were x/y, y is not 0, and x was known to be 0, the answer would be 0.
To say that x/y = n means that n*y = x.  If x is 0, then n needs to be 0 since y is some number.

numerator<>0, denominator=0
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If y/x is seen, y is not 0, then y/x = ±∞, depending on the sign of y.
This is because no matter how large a number is multiplied by x (which is 0), 0 is the reslut.

numerator=0, denominator=0
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If x/x is seen, then the answer is 0/0.  If 0/0 is gotten, there must be some factor in the numerator and denominator that can be factored out.  If the problem were to find the value of
(x²-3x-4)/(x²-7x+12) at x = 4, 0/0 is gotten at first.
Noting that the numerator is (x-4)(x+1) and the denominator is (x-4)(x-3),
the x-4 can be cancelled, since it is in both.  The result is (x+1)/(x-3).
Now we can put in x=4 and get (4+1)/(4-3) = 5/1 = 5.


Now that I have stated that, it can be seen that if the numerator is 0,
it doesn't matter unless the denominator is 0 as well.  
If the denominator is 0 as well, look for a common factor.