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### Simplifying an Algebraic Fraction

```
Date: 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/
```
Associated Topics:
Middle School Algebra

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