Simplifying an Algebraic FractionDate: 05/09/2000 at 12:49:43 From: M. Hancock Subject: Algebraic complex fractions Dear Dr. Math: I am retaking algebra with my 7th grade son (we are homeschoolers), and I am stuck on this type of problem: 1 + 1/(x + 1/x) I am to simplify this. The answer given in the book is: (x^2 + x + 1)/(x^2 + 1) I have tried x as a common denominator with the one just hanging out there. I get the denominator, but can't seem to get the x term in the numerator. The book calls this "complex fractions." M. Hancock Date: 05/09/2000 at 16:24:01 From: Doctor Wilkinson Subject: Re: Algebraic complex fractions Hi. Let's take it step by step. Ignoring the first term for the time being, we have: 1 --------- x + 1/x Let's start by simplifying the denominator. That means putting it over a common denominator x (you were doing fine so far). This should give you a denominator of: x^2 + 1 --------- x Now you have 1 over that, so flip it upside down to get: x --------- x^2 + 1 Now you have 1 + that, so you want now to make x^2 + 1 the common denominator, which gives you: x^2 + 1 + x ------------- x^2 + 1 or: x^2 + x + 1 ------------- x^2 + 1 - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/ |
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