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Complex Fractions: Technicalities

I started with this:

• Simplify the following expression:

...and ended up with this:   Copyright © Elizabeth Stapel 2003-2011 All Rights Reserved

The first two domain restrictions were easy. The sub-fraction in the complex fraction's numerator will be undefined if x – 1 = 0, and the sub-fraction in the denominator will be undefined if x + 4 = 0. The other restriction is harder. I had to consider the entire denominator. This would be zero when the numerator (of the denominator) was zero. Converting to a fraction, I got this:

The denominator will be zero when x2 + x – 11 is zero. Solving, I get:

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