Solve the equation #1/(x+1)+1/(x+5)=1/(x+4)+1/(x+2)#?

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Answer 1 · 2017-11-09T07:18:25

#x=-3#

As #1/(x+1) + 1/(x+5) = 1/(x+4) + 1/(x+2)#, we can write it as

#1/(x+1)-1/(x+2)=1/(x+4)-1/(x+5)#

i.e. #(x+2-(x+1))/((x+1)(x+2))=(x+5-(x+4))/((x+4)(x+5))#

or #1/((x+1)(x+2))=1/((x+4)(x+5))#

or #(x+1)(x+2)=(x+4)(x+5)#

or #x^2+3x+2=x^2+9x+20#

or #3x-9x=20-2#

or #-6x=18#

i.e. #x=18/(-6)=-3#