It all depends on the correct interpretation of the question. I have given two interpretations to demonstrate some mathematical processes. Even if they are not the correct solutions #color(magenta)("the methods are important.")#
You state #m+2/3+1/4m-1# and you use the word 'solve'. This implies that you wish to determine the value of #m#.
As there is no equals sign it is not possible to 'solve' for #m#
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#color(blue)("Taking the work on from your part 'solution'")#
#color(green)(12m+8=3m-1)#
subtract #color(red)(3m)# from both sides
#color(green)(12mcolor(red)(-3m)+8" "=" "3mcolor(red)(-3m)-1)#
#color(green)(" "9m" "color(white)(.)+8" "=" "0" "-1)#
Subtract #color(red)(8)# from both sides
#color(green)(9m+8color(red)(-8)" "=" "-1color(red)(-8)#
#color(green)(9m" "+0" "=" "-9)#
Divide both sides by #color(red)(9)#
#color(green)(9/(color(red)(9)) m" "=" "(-9)/(color(red)(9)))#
but #9/9=1 and (-9)/9=-1#
#color(green)(1m=-1)#
but writing #1m# is bad practice so write this as just #m#
#m=-1#
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#color(blue)("Assuming that we have an expression and not an equation")#
An expression does not have an equals sign in it.
Simplifying the expression# -> m+2/3+1/4m-1#
Note that #m# is the same as #1m# which is also the same as #4/4m#
#m+2/3+1/4m-1" "->" "4/4m+2/3+1/4m-1#
#" "->" "4/4m+1/4m+2/3-1#
#" "->" "5/4m+2/3-1#
Note that #-1# is the same as #-3/3#
#5/4m+2/3-1" "->" "5/4m+2/3-3/3#
#" "->" "5/4m-1/3 larr" Simplified"#
