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

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Answer 1 · 2015-05-27T03:23:43

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

cross multiplying

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

splitting the middle term and factorising the expression:
$x^2 - 3x +1x- 3 = 0$
$x(x-3) + 1(x-3) = 0$
$(x+1)(x-3) =0$

the solutions for the equation are $color(red)(x=-1 and x=3$

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