Quick math question, Got the answer just need help solving the problem?

Mark's Method is 100% correct. But I have got another way to go ahead. --

......... 2...............1.............2 x

=> ----------- - -------------- = -------------

.....(x + 1)....... ( x - 1 ). .. . .x² - 1

......... 2...............1.................2 x

=> ----------- - -------------- = -------------------

.....(x + 1)....... ( x - 1 ). . . . (x-1).(x+1)

Multiply the whole eqn by (x-1).(x+1) we get ---

=> 2 ( x - 1 ) - 1 ( x + 1 ) = 2 x

=> 2 x - 2 - ( x + 1 ) - 2 x = 0

=> 2 x - 2 - x - 1 - 2 x = 0

=> x = - 3 ............... Answer Answer

>>>>>>>>>>>>>>>>>

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You need to recognize that (x+1)(x-1) = (x^2-1) is a difference of two squares, so multiplying by (x^2-1)/(x^2-1) on both sides for every term makes it so that:

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

equals

(2)(x-1) - (1)(x+1) = 2x

equals

2x - 2 - x - 1 = 2x

x - 3 = 2x

-3 = x

Then you check by plugging -3 back in to make sure it's extraneous, but of course it's not because there's nothing in the denominator that makes it undefined. ;)

you may factor each and every. 2x + 2y = 10 2 (x + y) = 2 (5) x+y = 5 -2x - 2y = 4 -2 (x + y) = -2 (-2) x + y = -2 you have an impossible gadget. x + y won't be able to equivalent 5 AND - 2. So the gadget has no recommendations.