How do you solve #(3x+2)/x = (4x-2)/(3x) + 1/3#?

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Answer 1 · 2017-02-02T11:43:31

#"The answer is x=-2"#

#"given "(3x+2)/x=(4x-2)/(3x)+1/3#

#color(red)(3/3 )((3x+2)/x)=(4x-2)/(3x)+color(red)(x/x)1/3#

#(9x+6)/(3x)=(4x-2)/(3x)+x/(3x)#

#(9x+6)/(cancel(3x))=(4x-2)/(cancel(3x))+x/(cancel(3x))#

#9x+6=4x-2+x#

#9x+6=5x-2#

#9x-5x=-2-6#

#4x=-8#

#x=-8/4#

#x=-2#

Answer 2 · 2017-02-02T12:11:08

#x=-2#

#(3x+2)/x=(4x-2)/(3x)+1/3#

Multiply both sides by#3x#

#:.3(3x+2)=4x-2+x#

#:.9x+6=4x-2+x#

#:.9x-4x-x=-6-2#

#:.4x=-8#

#:.x=-8/4#

#:.x=-2#

Substitute #x=-2#

#:.(3(-2)+2)/-2=(4(-2)-2)/(3(-2))+1/3#

#:.(-6+2)/-2=(-8-2)/-6+1/3#

#:.-4/-2=-10/-6+1/3#

#:.2=-5/-3+1/3#

Multiply both sides by 3

#:.6=-5/-1+1#

#:.6=5+1#

#:.6=6#