How do you solve #3/(2x-9)-2=(5x)/(2x-9)# and check for extraneous solutions?

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Answer 1 · 2016-09-09T14:43:24

#x=7/3#

First you have to find the least common denominator #LCD# that is:

#2x-9#

Now, a denominator cannot be zero, then:

#2x-9!=0 => x!=9/2#

#:. x=9/2 !in FE# (Field of existence of the equation), and it cannot be a solution.

Now, you simplyfy the equation using the #LCD#

#(3-2(2x-9))/cancel((2x-9))=(5x)/cancel((2x-9))#

#=> 3-4x+18=5x#

Now move all the x therms in the LHS and the other in the RHS

#-4x-5x=-21#
#-9x=-21#
#9x=21#
#x=cancel(21)^7/cancel(9)^3=7/3#

with #x in FE#