SOLUTION: Please Simplify and give Restrictions. x^2 - y^2 / x^2 + 3xy + 2y^2 Thank you for your help! :)

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Question 725391: Please Simplify and give Restrictions.
x^2 - y^2 / x^2 + 3xy + 2y^2
Thank you for your help! :)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
this factors to:

(x-y)(x+y) divided by (x+2y)(x+y)

the (x+y) in the numerator and denominator cancel out and you are left with:

(x-y) divided by (x + 2y)

that's the simplified expression.

the restrictions come from the original equation.

the original equation is:

(x^2 - y^2) divided by (x^2 + 3xy + 2y^2) which factored out to be:

(x - y) * (x + y) divided by (x + y) * (x + 2y)

since the denominator can't be equal to 0, then the following restrictions apply.

x cannot be equal to -y, otherwise (x + y) will be equal to 0.

x cannot be equal to -2y, otherwise (x + 2y) will be equal to 0.