Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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Common Algebra II Mistakes - Problem 1

Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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A common mistake that Algebra 2 students make is whenever we’re dealing with a rational expression and we’re trying to simplify this, what students really like to do is just distribute your denominator to one term. This 4 would go wither to just the 4x or just the 8 leaving the other one t be however it is. I see it a lot where students would cancel the 4 here leaving us with x plus 8.

To show you an example of this, I’m going to go to just numeric example. If we have 9 plus 12 over 3, you know that your order of operations tells you to add these first because those are really in sort of an invisible parentheses. What we have is 9 plus 12, 21 divide by 3 which is 7. If we were to cancel this 3 with just one of these terms, say with the 9, we would end up with 3 plus 12 which is 15. Likewise if we cancel the 3 with the 12, we would end up with 4, we would end up with 9 plus 4, 13. Neither one is equal to the 7 that we should end up getting.

Whenever we have this fraction, this 4 has to end up going to both the 4x and the 8. So what we end up with is 4x over 4 which is equal to x and 8 over 4 which is equal to 2. Whenever we’re dealing with this fraction, make sure you distribute this denominator t both terms not just one.

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