## ← The Different Expression 2 - Visualizing Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

1. We know this is the answer. This rational expression is the odd one out, since
2. it equals positive 1. This expression over here is really equal to negative 1,
3. since x minus 7 divided by the quantity x minus 7 simplifies to 1. We get a
4. negative 1 since we have a negative sign sitting out here. This is really
5. negative 1 times 1. For this first rational expression, we can switch the order
6. of the denominator. I can have the negative x come first, and then followed by
7. the positive 7. We can see that this expression is the same as this last
8. expression down here. But this doesn't quite look like negative 1. But these two
9. rational expressions don't look like negative 1, but in fact, they are. We know
10. these expressions in the numerator and denominator are opposite polynomials. The
11. x terms are opposite in sign, as are the constant terms. We can factor a
12. negative 1 from our denominator to get negative 1 times x minus 7. Then we can
13. simplify our common factors in the numerator and denominator, leaving us with
14. negative 1. Nice thinking if you found that one.