How do you solve #\frac { x } { 2- x } - \frac { 2} { x + 2} - \frac { 1} { x ^ { 2} - 4} = 0#?

1 Answer
iceman
Apr 14, 2017

#x=-2+-sqrt7#

Explanation:

#x/(2-x)-2/(x+2)-1/(x^2-4)=0#
#-x/(x-2)-2/(x+2)-1/[(x-2)(x+2)]=0#
#[-x(x+2)-2(x-2)-1]/[(x-2)(x+2)]=0# , #(x!=+-2)#
#-x^2-2x-2x+4-1=0#
#-x^2-4x+3=0#
#x^2+4x=3#
#x^2+4x+4=3+4#
#(x+2)^2=7#
#x+2=+-sqrt7#
#x=-2+-sqrt7#

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