Do all rational equations have a single solution? Why is that so?
Whenever you solve a rational equation you must make sure the result obtained for an answer does not allow the denominator of one of the rational expressions to assume a value of ZERO, [ as division ...
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User: Do all rational equations have a single solution? Why is that so?

Note: All rational equations have at least one solution but they do not have just one solution there can be many.

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Weegy: Whenever you solve a rational equation you must make sure the result obtained for an answer does not allow the denominator of one of the rational expressions to assume a value of ZERO, [ as division by zero is undefined and therefore prohibited. For example if we have 2x/(x-3) =(x2 -9x)/ x when we multiply out by x(x-3) we get 2x(x) = (x2 -9x)(x-3) so 2x2 = x(x-9)(x-3) 2x2 = x(x2 - 12x + 27) 2x2 = x3 - 12x2 + 27x so 0 = x3 - 14x2 + 27x 0 = x(x2 - 14x + 27) so solutions are 0 and 7 + v22 and 7 -v22 but 0 makes right hand side expression have zero in denominator so it is not a solution. We actually have to look at all obtained solutions to be sure they ae not extraneous. Suppose we had obtained a 3 for a solution. That would make the left side denominator equal zero and we would have to dismiss that, if 3 was obtained. The two irrational solutions we have obtained are genuine solutions as neither introduces a zero to a denominator Read more: http://wiki.answers.com/Q/What_situation_would_one_or_more_solutions_of_rational_equation_be_unacceptable#ixzz20FoJFX4K ]

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