a) B = \(\left(\frac{x-4}{x\left(x-2\right)}+\frac{2}{x-2}\right):\left(\frac{x+2}{x}-\frac{x}{x-2}\right)\)
B = \(\left(\frac{x-4+2x}{x\left(x-2\right)}\right):\left(\frac{x^2-4-x^2}{x\left(x-2\right)}\right)\)
B = \(\left(\frac{3x-4}{x\left(x-2\right)}\right).\left(\frac{x\left(x-2\right)}{-4}\right)\)
B = \(\frac{3x-4}{-4}\)
b) Khi x = 2 thì B = \(\frac{6-4}{-4}\) = \(\frac{-1}{2}\)
c) Ta có: |B| - 2x = 5
⇔ \(\left|\frac{3x-4}{-4}\right|\) - 2x = 5
TH1: B ≥ 0 nếu 3x - 4 ≤ 0 ⇔ x ≤ \(\frac{4}{3}\)
⇔ \(\frac{3x-4}{-4}\) - 2x = 5
⇔ 3x - 4 + 8x = -20
⇔ 11x = -16
⇔ x = \(\frac{-16}{11}\) (t/m)
TH2: B ≤ 0 nếu 3x - 4 ≥ 0 ⇔ x ≥ \(\frac{4}{3}\)
⇔ \(\frac{3x-4}{4}-2x=5\)
⇔ 3x - 4 - 8x = 5
⇔ -5x = 9
⇔ x = \(\frac{-9}{5}\) (loại)
Vậy nghiệm của pt là x = \(\frac{-16}{11}\)
