In other words dont make the following mistake 4x 3 4x

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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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