x^3+4x/x^2-16 ÷ x^2+8x+15/x^2+x-20

[znick46]

x^3+4x/x^2-16 ÷ x^2+8x+15/x^2+x-20

Hi,
The question is to multiply or divide then simplify.

First i've flipped the second set of polynomials and multiplied everything

x^3+4x/x^2-16 multiplied x^2+x-20/x^2+8x+15

Receiving x^5+x^4-16x^3+4x^2-80x/x^4+8x^3-x^2-128x-240

Second I collect like terms

Third I divided receiving my final answer of x^5+5x^2-48x+240/24x^3

I'm of course wrong and utterly confused on where I went wrong. Can someone explain step by step, and when to factor/simplify?

Thank You

 

[Deleted member 4993]

Hi,
The question is to multiply or divide then simplify.

First i've flipped the second set of polynomials and multiplied everything

x^3+4x/x^2-16 multiplied x^2+x-20/x^2+8x+15

Receiving x^5+x^4-16x^3+4x^2-80x/x^4+8x^3-x^2-128x-240

Second I collect like terms

Third I divided receiving my final answer of x^5+5x^2-48x+240/24x^3

I'm of course wrong and utterly confused on where I went wrong. Can someone explain step by step, and when to factor/simplify?

Thank You

First of all you need to post problem correctly - using PEMDAS and grouping symbols like () or {} or [].

I think your problem is:

\(\displaystyle \displaystyle{\dfrac{x^3+4x}{x^2-16} * \dfrac{x^2+x-20}{x^2+8x+15}}\)

if that is correct then you should have posted it as follows:

(x^3+4x)/(x^2-16) * (x^2+x-20)/(x^2+8x+15)

If that is correct - then easiest way go about the problem is to factorize each of the numerators and the denominators

x³ + 4x = x (x² + 4)

x² - 16 = x² - 4² = (x+4)(x-4)

x²+x-20 = (x+5)(x-4)

and so on...

Then eliminate common-factors and then multiply.

Your way of multiplying is correct - but fraught with chances of many mistakes on the way ....

 

[znick46]

Sorry for the confusion.

Your notation of the question is correct.

How did you cancel out like terms then multiply with x(x^2+4) / (x+4)(x-4)?

Can you factor anytime for any equation? How do you know that you can factor at the beginning of the equation, and not to do it in the middle or the end?

Can you please carry out the rest of the question.

Thank You

 

[Deleted member 4993]

Sorry for the confusion.

Your notation of the question is correct.

How did you cancel out like terms then multiply with x(x^2+4) / (x+4)(x-4)?

Can you factor anytime for any equation? How do you know that you can factor at the beginning of the equation, and not to do it in the middle or the end?

Can you please carry out the rest of the question.

Thank You

Again you are not using grouping symbols!!

you wrote x(x^2+4) / (x+4)(x-4) which translates to x(x^2+4) / (x+4) * (x-4) or\(\displaystyle \dfrac{x(x^2+4)}{x+4}(x+4)\)

Is that what you wanted to write?

Did you factorize the remaining polynomial? → x^2+8x+15 [edit]

To review simplification of rational polynomials - go to:

http://www.purplemath.com/modules/rtnlmult2.htm

 

[znick46]

This is where i'm at

[x(x^2+4)]/[(x+4)(x-4)] * [(x+5)(x-4)]/[(x+3)(x+5)]


Can you factor anytime for any equation? What is the order of operation for factoring?

Can you please carry out the rest of the question.

 

[Deleted member 4993]

This is where i'm at

[x(x^2+4)]/[(x+4)(x-4)] * [(x+5)(x-4)]/[(x+3)(x+5)]


Can you factor anytime for any equation? What is the order of operation for factoring?

Can you please carry out the rest of the question.

Now do you recognize common factors between the numerators and the denominators. For example, one common factor is (x-4).

We can eliminate that and get:

x(x^2+4)/(x+4) * (x+5)/[(x+3)(x+5)] ........... [edit: took out some unnecessary brackets - for clarity] .

Do we have any other common factor/s?

 

[stapel]

Can you please carry out the rest of the question.

You already have loads of worked examples in your book, in your class notes, and on the various web pages you've reviewed. So one more worked example isn't going to make the difference. At some point, you need to start working the exercises.

...unless, of course, you're just wanting people to do the homework for you. In which case, you need to find a site that offers that service. It should be noted, though, that such sites are often ("usually"?) scams (since cheating attracts cheaters), so you'll want to use a credit card with a very low limit, so you won't lose much money if you contract with one of those sorts of sites.

If that's wrong and you are wanting to learn, then please start with the hints and helps with which you've already been provided. Then please reply showing (using clear notation) what you've done and where you're stuck. Thank you!