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÷ ( x + 1) = ç 4 ÷ ( x + 1)
x +1 ø
è x +1ø
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
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- Spring '12