Complex Fractions: Technicalities I started with:
...and ended up with: To get this "x not equal to zero" restriction, I had to consider all of the denominators, both of the entire fraction and of the subfractions. The two subfractions were the 1/x and the 2/x^{2} in the numerator and denominator: Copyright © Elizabeth Stapel 20032011 All Rights Reserved and Each of these expressions is undefined if x = 0. Then I also have to consider the denominator of the whole complex fraction. Recall that this was rearranged to be: A fraction is zero when its numerator is zero, so the above fraction would make the complex fraction undefined when 3x^{2} + 2 = 0. However, this is never equal to zero, so I got no further restrictions on my answer. Note: If you're going to have to find these restrictions on your answers, you may want to stick with the "flipnmultiply" method of simplification, instead of the "multiply through by the common denominator" method, since you'll need to convert the complex fraction's denominator into a fraction anyway. If you don't have to find these restrictions, be grateful, and don't worry about these notes on the rest of the examples in this lesson.



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