Answer:
choice 1) x = 2,3
Step-by-step explanation:
2x/(x - 2) - (x + 3)/(x - 4) = -4x/(x² - 6x + 8)
Factor x² - 6x + 8 into (x - 2)(x - 4):
2x/(x - 2) - (x + 3)/(x - 4) = -4x/(x - 2)(x - 4)
multiply both sides of the equation by (x - 2)(x - 4):
2x(x - 4) - (x + 3)(x - 2) = -4x
simplify:
2x² - 8x - x² + 2x - 3x + 6 = -4x
combine like terms:
x² -9x + 6 = -4x
add 4x to each side:
x² -5x + 6 = 0
factor:
(x - 3)(x - 2) = 0
x = 2, x = 3
