0<X<Y What does (X+Y)^2/(X-Y)^2 = (1) X^2 +Y^2 = 3XY

x^2 +2xy +y^2/x^2 - 2xy +y^2

using statement (1) we replace X^2 +Y^2 with 3XY and after that solve the equation.

Answer is A

Sorry Sergey..Thanks for your patience.


What if the problem was..


x + 2xy + y/ x - 2xy + y

Are we able to cancel out the x's and y's to get 4xy or must we factor first in order to cancel?

If we have an equation x + 2xy + y/ x - 2xy + y and
statement (1) says x+y=3xy for example than we would be able to substitute
(x+y) with 3xy and rewrite the equation as 3xy+2xy/3yx-2xy and get
5xy/xy where we can cancel out xy and get 5 as an answer

Let me know if it makes sense.

Yeah- I think I understand this problem, but I am now a little confused with other problems that look similar. This problem just triggered my confusion. I think you've helped to answer my questions by talking through it, but I want to make sure if the equations were different. For example,

x-y/x+y = 6

In the equation above we cancel out the x's and get 2y=6.

When we have a problem like the one we've been discussing in previous posts, my gut tells me to cancel out the x's and cancel out the y's (similar to the problem above except we have x^2 and 2xy)) and then take 2xy - (-2xy) to get 4xy. Guess I'm asking...can we only factor out x's and y's when we have single variable as above?

So if we had and wanted to solve for Y

x^2 + y^2/ x^2 -y^2 = 24

I know this can be factored out and we solve for y.
(x+y)(x+y)/(x+y)(x-y) = 24
= 2y=24 y=12

but when we add 2xy to the equation directly above my gut is telling me to subtract similar to the approach taken when we have the same equation as a power

2^(x+y)^2/2^(x-y)^2

Here we distribute and subtract to get 2^4xy. Sorry if I'm not making any sense..just trying to decipher between different formulas, factoring, canceling etc. I think I understand, just want clarification from someone who is more familiar.

x-y/x+y = 6 you can't cancel x's out because it's not a multiplication
you can cancel out only when there is * or /
for example 2xy/3x= 2y/3

So if we had and wanted to solve for Y

x^2 + y^2/ x^2 -y^2 = 24

(x+y)(x+y)/(x+y)(x-y) = 24 we can cancel only (x+y) and get x+y/x-y=24 and we'd need one more equation to solve it.

Thanks for your patience...I think I've got it now. I've been working with Exponent formula only- adding subtracting, etc for the last couple of weeks and had forgotten some basic non exponent formula rules.

you can't factor x + 2xy + y/ x - 2xy + y !!

if you try and factor with x you get:

x(1+2y) + y/x(1-2y) + y

and if you try and factor with y you get:

x + (2x+1)/x-(2x+1) + x