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#.