First, multiply each side of the equation by #color(red)(9.3)color(blue)(x)#. This is the common denominator for the two fractions and will eliminate the fractions while keeping the equation balanced:
#color(red)(9.3)color(blue)(x) xx 6.4/x = color(red)(9.3)color(blue)(x) xx 2.56/9.3#
#color(red)(9.3)cancel(color(blue)(x)) xx 6.4/color(blue)(cancel(color(black)(x))) = cancel(color(red)(9.3))color(blue)(x) xx 2.56/9.3#
#color(red)(9.3) xx 6.4 = color(blue)(x) xx 2.56#
#59.52 = 2.56x#
Now, divide each side of the equation by #color(red)(2.56)# to solve for #x# while keeping the equation balanced:
#59.52/color(red)(2.56) = (2.56x)/color(red)(2.56)#
#23.25 = (color(red)(cancel(color(black)(2.56)))x)/cancel(color(red)(2.56))#
#23.25 = x#
#x = 23.25#
