You can
put this solution on YOUR website!
.
Just look at the denominator in the expression and recall that division by zero is never permitted.
.
That being the case, you can't allow the denominator to be zero. But the denominator
would become zero if either of the factors were equal to zero.
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The first factor would equal zero if:
.
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Adding +5 to each side would result in:
.
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and dividing both sides by 4 finally tells you that:
.
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So if x = 5/4 the first factor in the denominator is zero, and this makes the entire
denominator equal to zero. Since this is not permitted, you can't allow x to be
.
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On to the second factor in the denominator, namely
. It also can't equal zero.
Set
equal to zero and solve for x.
.
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Subtract 1 from both sides and you get:
.
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That's all there is to it ... you cannot allow x to be
or
. If you were
to graph the original expression, as the value of x began to approach either of these two
values, the value of y would explode upward or downward towards infinity ... the direction
depending on the sign and direction that the value of x was approaching from.
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Hope this helps you understand the process.
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