Given:#" "color(brown)(1/3=(2x+2)/(2x-1))#
#color(green)("Multiply both sides by "color(blue)(3))#
#" "color(brown)(1xx(color(blue)(3))/3 =(color(blue)(3)(2x+2))/(2x-1)#
#color(green)("But "3/3 = 1" giving")#
#" "color(brown)(1=(6x+6)/(2x-1))#
#color(green)("Multiply both sides by "color(blue)((2x-1)))#
#" "color(brown)(1color(blue)(xx(2x-1)) = (6x+6)xx(color(blue)(2x-1))/(2x-1)#
#color(green)("But "(2x-1)/(2x-1)=1" giving")#
#" "color(brown)(2x-1=6x+6)#
#color(green)("Subtract "2x" from both sides giving:")#
#" " color(brown)(0-1=4x+6)->"Note that "6x-2x=4x#
#color(green)("Subtract 6 from both sides giving")#
#" "color(brown)( -7=4x)#
#color(green)("Divide bot sides by 4 giving")#
#" "color(brown)(-7/4=x)#
#" "color(blue)(x=-7/4)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
#(2x+2)/(2x-1) -> (2(-7/4)+2)/(2(-7/4)-1)= (-3/2)/(-9/2) =+ (3/2xx2/9) =3/9=1/3#
#color(red)("Confirmed as correct!")#
