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# S95-35

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Math Expert
Joined: 02 Sep 2009
Posts: 95674
Own Kudos [?]: 660393 [0]
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Math Expert
Joined: 02 Sep 2009
Posts: 95674
Own Kudos [?]: 660393 [1]
Given Kudos: 87330
Joined: 02 Oct 2014
Posts: 9
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Joined: 10 Jan 2017
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Easier perhaps (if I'm correct):

$$\frac{1}{x^2−y^2} - \frac{1}{x^2+2xy+y^2}$$

which is the same than: $$x^2+2xy+y^2 = x^2−y^2$$
hence $$(x+y)^2 = x^2−y^2$$
and $$(x+y) (x+y) = x^2−y^2$$

Statement (1) $$2y = x^2−y^2$$
Therefore $$(x+y)^2 = 2y$$

Statement (2) $$x+y = 4$$
Therefore $$4 * 4 = 2y$$

Which finally gives $$y = 8$$

Joined: 01 Nov 2016
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Concentration: Technology, Operations
marinlst
Easier perhaps (if I'm correct):

$$\frac{1}{x^2−y^2} - \frac{1}{x^2+2xy+y^2}$$

which is the same than: $$x^2+2xy+y^2 = x^2−y^2$$

marinlst, I do not think that is correct. According to that logic, 1/4 - 1/2 would be the same as 4=2, which is not right.

This is an extremely hard question. The official answer says that you must simplify the original equation to $$\frac{2y}{(x-y)(x+y)^2}$$. I was close but I couldn't finish in time. When I combined the two denominators, I ended up with : $$\frac{(x+y)^2-(x+y)(x-y)}{(x+y)^3(x-y)}$$. I didn't know what to do from this point, but if I had factored out (x+y) from both the top and bottom I would have eventually gotten $$\frac{(x+y)-(x-y)}{(x+y)^2(x-y)}$$ which simplifies to $$\frac{2y}{(x+y)^2(x-y)}$$ which would have made it very easy to see the correct answer.

Is completely solving out the equation really the fastest way to the answer? I tried to use guess and check but that didn't work. I guessed with value x=0 and got y=0,-2 for statement 1 and y=4 for statement 2, which doesn't make sense.
Joined: 26 Apr 2018
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