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

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Answer 1 · 2016-04-10T05:16:07

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

Cross Multiply:

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

$x(x-2)=3$

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

What we now have is a quadratic equation:
We can now factor this further:

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

Now we can solve by using the null factor law (that is, determining the numbers that make each bracket =0):

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

Solution 1:
$color(red)((3-3))(3+1)=0$
$0*4=0$
$0=0$
Therefore, one solution to the equation is $x=3$

Solution 2:
$(1-3)color(red)((-1+1))=0$
$-2*0=0$
$0=0$
Therefore, the other solution to the equation is $x-1$

Therefore, $x=3$ or $x=-1$ .

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