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