SOLUTION: Good evening (here): If may I'd like to give you a bit of background on myself. I'm a 78 yr. old man, retired medical technologist. I recently got the idea I'd like to learn calcu

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Good evening (here): If may I'd like to give you a bit of background on myself. I'm a 78 yr. old man, retired medical technologist. I recently got the idea I'd like to learn calcu      Log On


   

Question 1175007: Good evening (here):
If may I'd like to give you a bit of background on myself. I'm a 78 yr. old man, retired medical technologist. I recently got the idea I'd like to learn calculus. I discovered free e books on Amazon. I got the precalculus book and soon figured out that I needed to go back to Algebra. So I got their intermediate algebra book.
I'm now studying multiplying rational functions. Regarding the problem:
x^2-x/3x^2+27x-30*x^2-100/x^2-10x. I did all the factoring and multiplying, and canceling and came up with an answer of 3. The book and all my other resources ( Math papa, Microsoft problem solver and this site) say the answer is 1/3. What I would like to know is, what is this procedure called
for finding this solution, why use it now, and when is it necessary to use it. I can find no information on this solution procedure.
I can be reached at ledfrn@gmail.com. I thank you in advance for your attention to this matter. Roy Ledford
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If may I'd like to give you a bit of background on myself. I'm a 78 yr. old man, retired medical technologist. I recently got the idea I'd like to learn calculus. I discovered free e books on Amazon. I got the precalculus book and soon figured out that I needed to go back to Algebra. So I got their intermediate algebra book.
I'm now studying multiplying rational functions. Regarding the problem:
x^2-x/3x^2+27x-30*x^2-100/x^2-10x. I did all the factoring and multiplying, and canceling and came up with an answer of 3. The book and all my other resources ( Math papa, Microsoft problem solver and this site) say the answer is 1/3. What I would like to know is, what is this procedure called
for finding this solution, why use it now, and when is it necessary to use it. I can find no information on this solution procedure.
I can be reached at ledfrn@gmail.com. I thank you in advance for your attention to this matter.
------------------------
To start, x^2-x/3x^2+27x-30*x^2-100/x^2-10x is not a problem.
It's not an equation, there's no "solve for x."
It's likely it can be "simplified" but that's all.
---------------------
How did you come up with 3?

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


First, get used to using parentheses where necessary. The expression as you show it,

x^2-x/3x^2+27x-30*x^2-100/x^2-10x

means this:

x%5E2-x%2F3x%5E2%2B27x-30%2Ax%5E2-100%2Fx%5E2-10x

That's clearly not what you meant.

The expression you are working with is

((x^2-x)/(3x^2+27x-30))*((x^2-100)/(x^2-10x))

which means this:

%28%28x%5E2-x%29%2F%283x%5E2%2B27x-30%29%29%2A%28%28x%5E2-100%29%2F%28x%5E2-10x%29%29

Multiplying rational functions is just like multiplying numerical fractions. If you had, for example,

%2815%2F8%29%2A%2816%2F3%29

you could multiply the numerators and multiply the denominators and simplify the resulting fraction:

%2815%2F8%29%2A%2816%2F3%29+=+240%2F24+=+10

But it would be easier if you simplified the product before doing any multiplication:



When multiplying rational fractions you DEFINITELY want to factor the expressions and simplify where possible before performing any multiplication.

%28%28x%5E2-x%29%2F%283x%5E2%2B27x-30%29%29%2A%28%28x%5E2-100%29%2F%28x%5E2-10x%29%29



All the factors cancel except for the 3 in the denominator.

So if you got 3 for the answer, you made a mistake very popular among beginning algebra students. You saw that the only factor left was "3", so that was the answer. But the 3 that is left is in the denominator. You don't see it, but there is also a "1" left in the numerator, making the answer 1/3 instead of 3.

So it looks as if you did all the factoring and canceling of common factors correctly; you just didn't realize what the final simplified form was.