How do you solve the rational equation #(x-2)/3=1/x#?

Jan 1, 2016

#x=3" "# or #" "x=-1#

Cross multiply to get

#x^2-2x=3#

Rearrange to get

#x^2 -2x -3 =0#

Factor to get

#(x-3)(x+1)=0#

#{(x-3=0), (x+1=0) :} implies { (x=3), (x=-1) :}#

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