(2/3) = 2 - (5x-3)/(x-1)
2(x-1) = 6(x-1) - 3(5x-3) (multiply both sides by 3(x-1), the least common denominator)
2x -2 = 6x -6 -15x + 9 (use the distributive property to eliminate parentheses)
11x -2 = 3 (add 9x to both sides, collect terms)
11x = 5 (add 2 to both sides)
x = 5/11 (divide both sides by 11)
Check
2/3 = 2 - (5(5/11)-3)/((5/11)-1)
2/3 = 2 - (25/11 -33/11)/(5/11 -11/11)
2/3 = 2 - (-8/11)/(-6/11)
2/3 = 2 - 4/3
2/3 = 6/3 - 4/3 (yes)
2(x-1) = 6(x-1) - 3(5x-3) (multiply both sides by 3(x-1), the least common denominator)
2x -2 = 6x -6 -15x + 9 (use the distributive property to eliminate parentheses)
11x -2 = 3 (add 9x to both sides, collect terms)
11x = 5 (add 2 to both sides)
x = 5/11 (divide both sides by 11)
Check
2/3 = 2 - (5(5/11)-3)/((5/11)-1)
2/3 = 2 - (25/11 -33/11)/(5/11 -11/11)
2/3 = 2 - (-8/11)/(-6/11)
2/3 = 2 - 4/3
2/3 = 6/3 - 4/3 (yes)
