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

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Answer 1 · 2016-01-28T15:31:48

$x=-1,3$

Notice that the fractions on the left hand side have the same denominator, so they can be combined easily.

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

Now, we can cross multiply.

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

$x^2-2x=3$

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

This is factorable.

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

This can be split up, since we have two things being multiplied and equalling zero.

$x-3=0" "" ""or"" "" "x+1=0$

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

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