SOLUTION: What values for x must be excluded in the following fraction? {{{(x-3)/((4x-5)*(x+1))}}} I got a little confused on this problem and need some assistance. Thanks

Algebra ->  Radicals -> SOLUTION: What values for x must be excluded in the following fraction? {{{(x-3)/((4x-5)*(x+1))}}} I got a little confused on this problem and need some assistance. Thanks      Log On


   

Question 72948: What values for x must be excluded in the following fraction?
%28x-3%29%2F%28%284x-5%29%2A%28x%2B1%29%29
I got a little confused on this problem and need some assistance. Thanks
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%2F%28%284x-5%29%2A%28x%2B1%29%29
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Just look at the denominator in the expression and recall that division by zero is never permitted.
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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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4x+-+5+=+0
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Adding +5 to each side would result in:
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4x+=+5
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and dividing both sides by 4 finally tells you that:
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+x+=+5%2F4
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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 5%2F4.
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On to the second factor in the denominator, namely x+%2B+1. It also can't equal zero.
Set x%2B1 equal to zero and solve for x.
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x+%2B+1+=+0
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Subtract 1 from both sides and you get:
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x+=+-1
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That's all there is to it ... you cannot allow x to be 5%2F4 or -1. 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.