simplify [(x - y) / (x + y)] + [(x + y) / (x - y)]

Add those like you would add fractions:

1/2 + 2/7
 
what's wroing with this?

Solve: x-y/x+y + x+y/x-y

(x-y) (x-y)/(x+y)(x-y) + (x+y)(x+y)/(x+y)(x-y)

(x-y) + (x+y)

x-y+x+y

2x
 
not sure what to do next

now i came up with this answer--not sure whether this can be simplified further

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

can this be simplified further? x(x-y) / (x+y) ???
 
Re: not sure what to do next

Jodene222 said:
now i came up with this answer--not sure whether this can be simplified further

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

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

can this be simplified further? x(x-y) / (x+y) ???
Click to expand...
 
question

I see how the numerator is 2(x^2+y^2)

However, what happened to the (x+y)(x-y) in the denominator?

Can the x+y be factored out and the answer would then be
2(x+y)
_________
(x-y)
 
Re: question

Jodene222 said:
I see how the numerator is 2(x^2+y^2)

However, what happened to the (x+y)(x-y) in the denominator?

Can the x+y be factored out and the answer would then be

Absolutely not!

you cannot factor out (x+y) from the given numerator.


2(x+y)
_________
(x-y)
Click to expand...
 
YES, that's correct.

You can verify your answer by substituting values for x and y (like x=2 and y=1)
in both the original and your ending expression: if correct, you'll get same results.

original:
(2-1)/(2+1) + (2+1)/(2-1) = 1/3 + 3 = 10/3
your solution:
2(4+1) / ((2+1)(2-1)) = 2(5) / 3 = 10/3

CLEAR?
 
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