To add or subtract fractions both fractions must have common denominators. First, we will multiply the fraction on the left by the appropriate form of #1# to put both fractions over a common denominator of #8x# without affecting the value of the fractions:
#(color(red)(2)/color(red)(2) xx (3x + 7)/(4x)) - 15/(8x) =>#
#(color(red)(2)(3x + 7))/(color(red)(2) xx 4x) - 15/(8x) =>#
#((color(red)(2) xx 3x) + (color(red)(2) xx 7))/(8x) - 15/(8x) =>#
#(6x + 14)/(8x) - 15/(8x)#
We can now subtract the numerators over the common denominator:
#(6x + 14)/(8x) - 15/(8x) => ((6x + 14) - 15)/(8x) =>#
#(6x + 14 - 15)/(8x) =>#
#(6x - 1)/(8x)#
Or
#(6x)/(8x) - 1/(8x) =>#
#((2 xx 3)x)/((2 xx 4)x) - 1/(8x) =>#
#((color(red)(cancel(color(black)(2))) xx 3)color(blue)(cancel(color(black)(x))))/((color(red)(cancel(color(black)(2))) xx 4)color(blue)(cancel(color(black)(x)))) - 1/(8x) =>#
#3/4 - 1/(8x)#
