division of polynomials, help?

Well, division of fractions is the same as multiplication of the inverse.

(x² + 2xy - 3y²) (x² + 4xy + 3y²)

___________ ÷ ____________

(x² - 3xy + 2y²) (x² + 2xy - 8y²)

(x² + 2xy - 3y²) (x² + 2xy - 8y²)

___________ * ____________

(x² - 3xy + 2y²) (x² + 4xy + 3y²)

This link may help you on similar problems.

http://answers.yahoo.com/question/index;_ylt=AvY3u...

You use the same steps on problems of the form, "ax^2 + axy + cy^2" ((x² + 2xy - 3y²)) as the one from the link. You'll see the similarities if you study my walk through below and the one from the link.

I'll walk through it anyways:

(x² + 2xy - 3y²) (x² + 2xy - 8y²)

___________ * ____________

(x² - 3xy + 2y²) (x² + 4xy + 3y²)

(x² + 2xy - 3y²) is of the form: ax^2 + bxy + cy^2 or simpler: ax^2 + bx + c. same thing really..

a = 1, b = 2, c = -3

multiply the ends:

a*c

-3 * 1 = -3

Find the factors of -3: They are (3 and -1), (-3 and 1).

Middle term is 2, a positive number, so the bigger number (3) must also be positive: (try making the smaller number positive one time and you will see why the bigger number has to be positive if the middle term is positive)

x^2 + 3xy - xy - 3y^2

Group:

(x^2 + 3xy) + (-xy - 3y^2)

Pull out GCF:

1x(x + 3y) - 1y(x + 3y)

Distributive Property:

(x - y) (x + 3y)

Do all these steps to all four polynomials and cancel or use division like the other person did. Those are the steps. Simple and quick when you get some practice.

first make multiply by reciprocal:

(x^2 + 2xy - 3y^2) * (x^2 + 2xy - 8y^2)

-------------------------- -------------------------

(x² - 3xy + 2y²) (x² + 4xy + 3y²)

factor:

(x - y) (x + 3y) * (x - 2y) (x + 4y)

---------------------- -----------------------

(x - 2y) (x - y) (x + 3y) (x + y)

cancel:

x + 4y

---------

x + y

factor...and flip the second equation changing to mult.

(x + 3y) ((x - y) (x + 4y) (x - 2y)

____________ * ____________

(x - 2y) (x - y) (x + 3y) (x + y)

the factors that cancel (appearing both in numerator and denominator) are (x + 3y), (x - y), and (x - 2y) leaving

(x + 4y)

______

x + y