document.write( "Question 72948: What values for x must be excluded in the following fraction?
\n" ); document.write( " $\"%28x-3%29%2F%28%284x-5%29%2A%28x%2B1%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "I got a little confused on this problem and need some assistance. Thanks \n" ); document.write( "

Algebra.Com's Answer #52188 by bucky(2189) $\"\"$ $\"About$

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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\n" ); document.write( "Just look at the denominator in the expression and recall that division by zero is never permitted.
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\n" ); document.write( "That being the case, you can't allow the denominator to be zero. But the denominator
\n" ); document.write( "would become zero if either of the factors were equal to zero.
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\n" ); document.write( "The first factor would equal zero if:
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\n" ); document.write( " $\"4x+-+5+=+0\"$
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\n" ); document.write( "Adding +5 to each side would result in:
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\n" ); document.write( " $\"4x+=+5\"$
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\n" ); document.write( "and dividing both sides by 4 finally tells you that:
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\n" ); document.write( " $\"+x+=+5%2F4\"$
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\n" ); document.write( "So if x = 5/4 the first factor in the denominator is zero, and this makes the entire
\n" ); document.write( "denominator equal to zero. Since this is not permitted, you can't allow x to be $\"5%2F4\"$ .
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\n" ); document.write( "On to the second factor in the denominator, namely $\"x+%2B+1\"$ . It also can't equal zero.
\n" ); document.write( "Set $\"x%2B1\"$ equal to zero and solve for x.
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\n" ); document.write( " $\"x+%2B+1+=+0\"$
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\n" ); document.write( "Subtract 1 from both sides and you get:
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\n" ); document.write( " $\"x+=+-1\"$
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\n" ); document.write( "That's all there is to it ... you cannot allow x to be $\"5%2F4\"$ or $\"-1\"$ . If you were
\n" ); document.write( "to graph the original expression, as the value of x began to approach either of these two
\n" ); document.write( "values, the value of y would explode upward or downward towards infinity ... the direction
\n" ); document.write( "depending on the sign and direction that the value of x was approaching from.
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\n" ); document.write( "Hope this helps you understand the process. \n" ); document.write( "

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