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Unformatted text preview: there is no factoring to do so we can go straight to identifying where the numerator
and denominator are zero. numerator : x = 3
2 denominator : x = 4 Here is the number line for this problem. Okay, we want value of x that give positive and/or zero in the rational expression. This looks like
the outer two regions as well as x = 3
. As with the first example we will need to avoid x = 4
2 since that will give a division by zero error.
The solution for this problem is then, ¥ < x < 4 ( ¥, 4 )
Example 5 Solve and
and 3
£ x<¥
2
é3 ö
ê2 ,¥÷
ë
ø x 8
£ 3 x.
x Solution
So, again, the first thing to do is to get a zero on one side and then get everything into a single
rational expression. © 2007 Paul Dawkins 138 http://tutorial.math.lamar.edu/terms.aspx College Algebra x 8
+ x 3£ 0
x
x  8 x ( x  3)
+
£0
x
x
x  8 + x 2  3x
£0
x
x2  2 x  8
£0
x
( x  4 )( x + 2 ) £ 0
x
We also factored the numerator above so we can now determine where the numerator and
denominator are zero. numerator : x = 2, x = 4 denominator : x = 0...
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 Spring '12
 MrVinh

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