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#