How do you solve $(x - 2 )/ 3 = 1/x$ ?

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Answer 1 · 2016-06-19T08:37:34

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

Given:

$(x-2)/3 = 1/x$

Multiply both sides by $3x$ to get:

$(x-2)x = 3$

Expand the left hand side and subtract $3$ from both sides to get:

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

Factoring the left hand side we find:

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

So:

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

You can check these values by substituting back into the original equation:

$(3-2)/3 = 1/3$

$((-1)-2)/3 = -3/3 = -1 = 1/(-1)$

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