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

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Answer 1 · 2016-01-28T15:31:48

$x = - 1, 3$ $x=-1,3$

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

$\frac{x - 2}{3} = \frac{1}{x}$ $(x-2)/3=1/x$

Now, we can cross multiply.

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

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

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

This is factorable.

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

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

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

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

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