How do you solve #2/3 = 2 - (5x-3)/(x-1)#?

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Answer 1 · 2017-07-13T14:49:40

#color(magenta)(x=5/11=# extraneous solution

#2/3=2-(5x-3)/(x-1)#

#:.-(5x-3)/(x-1)=2/3-2#

multiply both sides by #-1#

#:.(5x-3)/(x-1)=-2/3+2#

multiply both sides by #x-1#

#:.5x-3=-2/3(x-1)+2(x-1)#

#:.5x-3=-2/3x+2/3+2x-2#

#:.5x+2/3x-2x=2/3-2+3#

#:.3 2/3x=3 2/3-2#

#:.11/3x=3 2/3-2#

#:.11/3x=1 2/3#

#:.11/3x=5/3#

#:.x=(5/3)/(11/3)#

#:.x=5/cancel3^1 xx cancel3^1/11#

#:.color(magenta)(x=5/11=# extraneous solution