How do you solve the rational equation $\frac{x - 2}{3} = \frac{1}{x}$ $(x-2)/3=1/x$ ?

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Answer 1 · 2016-01-01T00:50:17

$x = 3$ $x=3" "$ or $x = - 1$ $" "x=-1$

Cross multiply to get

$x^{2} - 2 x = 3$ $x^2-2x=3$

Rearrange to get

$x^{2} - 2 x - 3 = 0$ $x^2 -2x -3 =0$

Factor to get

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

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

How do you solve the rational equation (x-2)/3=1/xx−23=1x(x-2)/3=1/x?