1. ## Comparing Two Quantities

I have two quantities, A and B. I need to know which is larger or whether they are equivalent.

Quantity A: X^2 + 2xy +y^2/x + y
Quantity B: x + y + 2

Note: X + Y does not equal zero.

Thank you!

2. Originally Posted by wizkid94
I have two quantities, A and B. I need to know which is larger or whether they are equivalent.

Quantity A: X^2 + 2xy +y^2/x + y
Quantity B: x + y + 2

Note: X + Y does not equal zero.

Thank you!
if this is what you meant by quantity A ...

$\displaystyle \dfrac{x^2+2xy+y^2}{x+y}$

... factor the numerator and simplify, then compare.

3. I factored and I have x^2 + 2y for A, compared against x + y + 2 for B. My book says that quantity B is bigger. Why is this?

OK I think I might have made a mistake in factoring. In quantity, A, should x^2 still have the denominator of x + y? If this is so, by plugging in numbers, quantity does indeed prove to be bigger. So, I guess my question is when you cross out the x + y of the numerator after factoring, does the x^2 retain its denominator of x + y or does it also go?

4. is what "skeeter" wrote to you true ? is that what you meant by quantity A ?

5. Yes.

6. Originally Posted by wizkid94
Yes.
You needed BRACKETS then: (x^2 + 2xy +y^2) / (x + y) ; OK?

HINT: (x + y)(x + y) = ?

7. Originally Posted by Wilmer
You needed BRACKETS then: (x^2 + 2xy +y^2) / (x + y) ; OK?

HINT: (x + y)(x + y) = ?
That would equal the numerator, leaving us with x-y for Quantity A, and still x + y + 2 for B. But still, then, how do we know which quantity is larger? All we know is that x + y does not equal 0. Say X were 3 and y were -8. Quantity A would be larger.

8. Originally Posted by wizkid94
That would equal the numerator, leaving us with x-y for Quantity A,...
No: leaves Quantity A = x + y ; don't "rush" so much !

9. Originally Posted by Wilmer
No: leaves Quantity A = x + y ; don't "rush" so much !
Thank you, thank you. I have been doing math for 6 hours today so my brain is fried.