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Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.$\frac{a^{3}-a^{2}-a+1}{a^{2}-2 a+1}$

$a+1$$a \neq 1$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 2

Simplifying Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

McMaster University

Baylor University

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in this question were given this expression A cube minus a squared, minus a plus one. So what we're gonna do in this question? Oh, her the nor mater over my bad. A squared minus to a plus one. There you go. So we want to simplify this, and we want to find the values of pay where this function is not true. And that would be where the denominator equal zero. Well, first, let's simplify this. So I think the denominator just looks easier to simplify. So we're gonna start with that. What we can do is we could just factor that and it will be a minus one squared, and we can actually check that. If we multiply that through, we will get a square minus two equals one. Now, in the numerator, this looks a bit harder to factor. But there's actually really cool triggered. I'm gonna show you. So you have this a cube term in this negative a term or right over here. Then we have this negative a square term in a positive ones. We have negative a squared plus one. Now we can a fact or something in the a cubed minus a so that we get a squared plus one or negative a scrip us one. If we factor out a negative, eh? We will get negative a squared plus one. And if we just factor a one here, of course, it's just gonna be negative. A scripless one. Now, if you add these factors and multiply it by negative a script is one. That is how you factor this expression. So it'll just be negative. A simple, sworn soldiers, right as one minus squared times one mine is a and that's it. And actually, I think it's easier if we just take out the like a negative here. So instead of writing one, mine's a score times one minus a week in just right a minus one was putting negative right there and then one minus a squared. So now what can we cancel out? Weaken? You can see we can Kids allowed that a minus one thing. Kids love that factor right there, and we can multiply this negative end So we have we can write as a squared minus one instead of this woman is a square times of negative. So your face reminds one over a minus one and I'll Google any page or quick, so it's easier to see that. So right now we have a squared minus one over a minus one. We can factor that ice cream ice one again. So we get a minus one times eight plus one over a minus one. Divide these out and you get a close one. So that is your simplified expression. But we have to go back real quick and look at our denominator and say What are the values of a where this doesn't work? So of course, if we plugged in a equals one, we would get zero The denominator in this expression, we're not work. So even though we can end up simplifying into April's won, there is still the value of a equals ones. We say they cannot equal one where this expression would give you zero in the denominator

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