(x² + 2xy - 3y²) (x² + 4xy + 3y²)
___________ ÷ ____________
(x² - 3xy + 2y²) (x² + 2xy - 8y²)
i get confused on how to do this one. i need the steps on how to answer this and also the arrived answer so i can check my answer too. thanks!
Anonymous
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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=AvY3uo_bAqzeGgdv9no88F3ty6IX;_ylv=3?qid=20091107171048AAhMoWA&show=7#profile-info-Qcktv8baaa
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.
Tim M
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
Anonymous
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