Question

Hey, I have a simplification question that's bugging me. n^2+4n-21/n*n/3-n I have factored the expression to (n+7)(n-3)n/n(3-n) and am stuck when it comes to how to cancel the factors. I know the n cancels across.

Answer 1

Hint: (3-n) = -1(n-3)

Answer 2

I remember that, I am not sure what to do about the -1 that that will leave me on the bottom of the equation; we were told not to leave negatives in the denominator.

Answer 3

\[\frac{x}{-1y} = \frac{-x}{1y} = -\frac{x}{y}\]

Answer 4

im gathering that this means that the expression becomes -(n+7) in this case? (left out the 1 on the bottom for simplicity's sake)

Answer 5

Yes, or 7-n.

Answer 6

That. The 7-n. That makes sense! Expressions like that mess with me; (numerical dyslexia) so I'm not ever sure I'm looking at it properly. So if I were to work it the long way through: -1(n-7) => -n+7 => 7-n?

Answer 7

Or am I making some kind of fundamental error with that line of reasoning?

Answer 8

Yes, that's all correct.

Answer 9

You have my sympathy on the numerical dyslexia, it's easy enough to make mistakes without your brain playing tricks on you!

Answer 10

Thank you! You've been a big help, I've been stuck on that concept for some time now. I doubt myself whenever I see an expression like that and get hung up, knowing I can work it through the long way if I need to will be a big help!

Answer 11

If I can offer a suggestion, pay attention to where you make your mistakes, and see if there are patterns. You may find that there are things you can do to improve your accuracy. I know that I'm more likely to make mistakes when doing something like -3(x - 5 - b), so I go through those parts more slowly, and if there's a way to work the problem that avoids doing it altogether, I may do that. Sometimes making substitutions makes algebra simpler, even though it isn't necessary. Do what you can to stack the deck in your favor.

Answer 12

Of course I can offer a suggestion. If I may offer a suggestion... :-)

Answer 13

Of course! There are patterns. I switch #s around, doesn't matter where in the expression they came from I they just switch on the paper and I don't catch it til I've spent all the time working the problem, and I and lose signs like nobody's business (a la 3-n and n-3). Drives me crazy.

I originally factored the problem as n+7 and n-4 because I switched the 4n with my factors in the orig. expression and couldn't reduce it any further. Now I'm looking at it factored correctly and it makes much more sense.

Answer 14

Well, good luck. Feel free to shoot me a message if you get stuck on something, and I'll try to help. Time for me to go to the library...

Answer 15

Thanks! I will!