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Study Guide

You thought you were knee-deep in complexity up to now? Brace yourself. Welcome to the wacky world of complex rational expressions. These guys have fractions *inside* their fractions. They may drive you nuts if you think about them too long. Don't worry—you can simplify the complex. Just treat 'em like long division.

Simplify .

Looks scary? Chill. It's only long division. Rewrite it as a division problem.

Now flip and multiply.

Cancel like factors.

Which gives us:

Simplify .

Flip and switch to multiplication.

Factor and cancel.

And the answer is:

2(*x* – 1)

Simplify .

Before we flip the switch and proceed to multiplication, we gotta do the subtraction and addition in the numerator and denominator.

The numerator:

The denominator:

Now, rewrite the whole thing as a multiplication problem.

Factor the *a*^{2} – 1:

Cancel like factors.

That gives us the final answer, along with a well-earned victory dance:

*a* – 1

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