Giải các phương trình chứa ẩn ở mẫu: (x+1)/(x-1) - (x-1)/(x+1) = 16/(x²-1)

a) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{16}{x^2-1}\) (x ≠1, x≠-1)

<=>\(\left(x+1\right)\left(x+1\right)-\left(x-1\right)\left(x-1\right)=16\)

<=> \(x^2+2x+1-\left(x^2-2x+1\right)=16\)

<=> \(x^2+2x+1-x^2+2x-1=16\)

<=> \(4x\ =16\)

<=> x = 4

b) \(\frac{2}{x^2-4}-\frac{x-1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\) (đk: x≠2, x≠ - 2)

<=> 2x - (x - 1)(x +2) + (x - 4)(x - 2) = 0

<=> 2x - (x² + x - 2) + x² - 6x + 8 = 0

<=> 2x - x² - x + 2 + x² - 6x + 8 = 0

<=> - 5x + 10 = 0

<=> x = 2