How do you solve the equation and identify any extraneous solutions for #x/(x-2) - 5 = 2/(x-2)#?

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Answer 1 · 2015-06-09T14:45:21

This equation has no solutions.

Starting with:

#x/(x-2)-5=2/(x-2)#

subtract #2/(x-2)# from both sides to get:

#0 = x/(x-2)-2/(x-2)-5#

#=(x-2)/(x-2)-5#

#=1-5#

#=-4#

with exclusion #x != 2#