We need to talk about applications to linear

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Unformatted text preview: æ ç ÷ ( x + 1) = ç 4 ÷ ( x + 1) x +1 ø è x +1ø è 2 = 4 ( x + 1) - 2 x 2 = 4x + 4 - 2x 2 = 2x + 4 -2 = 2 x -1 = x So, we once again arrive at the single value of x that we needed to avoid so we didn’t get division by zero. Therefore, this equation has no solution. [Return to Problems] So, as we’ve seen we do need to be careful with division by zero issues when we start off with equations that contain rational expressions. At this point we should probably also acknowledge that provided we don’t have any division by zero issues (such as those in the last set of examples) linear equations will have exactly one solution. We will never get more than one solution and the only time that we won’t get any solutions is if we run across a division by zero problems with the “solution”. © 2007 Paul Dawkins 69 http://tutorial.math.lamar.edu/terms.aspx College Algebra Before leaving this section we should note that many of the techniques for solving linear equations will show up time and again as we cover different kinds of equations so it very im...
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