How do you solve #(x-1)/(x-2) - (x+1)/(x+2) = 4/(x^2-4)#?

1 Answer
Alan P.
Aug 24, 2017

There are no valid solutions to this equation

Explanation:

Note that #(x-1)/(x-2)-(x+1)/(x+2)=4/(x^2-4)# is only defined if #x!=+-2#

If we attempt to solve this equation by converting all terms to the common denominator of #(x-2)(x+2)=x^2-4#
we get
#((x-1)(x+2))/(x^2-4)-((x+1)(x-2))/(x^2-4)=4/(x^2-4)#

#rarr (x-1)(x+2)-(x+1)(x-2)=4#

#rarr (x^2+x-2)-(x^2-x-2)=4#

#rarr cancel(x^2)+xcancel(-2)cancel(-x^2)+xcancel(+2)=4#

#rarr 2x=4#

#rarr x=2#

BUT the original equation is not defined if #x=2#

Therefore there is no valid solution.

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