a) ĐKXĐ : x\(\ne\)2,-2,0
H = 1 - \(\frac{1}{x^2-4}\)[(\(\frac{4x-x^2-4}{4x}\)) : (\(\frac{2-x}{2x}\))
H = 1 - \(\frac{1}{x^2-4}\)[\(\frac{-\left(x-2\right)^2}{4x}\).\(\frac{2x}{-\left(x-2\right)}\)]
H = 1 - \(\frac{1}{x^2-4}\).\(\frac{x-2}{2}\)
H = 1 - \(\frac{1}{2\left(x+2\right)}\)
H = \(\frac{2\left(x+2\right)-1}{2\left(x+2\right)}\)
H = \(\frac{2x+4-1}{2x+4}\)
H = \(\frac{2x+3}{2x+4}\)
b) H = \(\frac{1}{4}\)
⇒ \(\frac{2x+3}{2x+4}\)=\(\frac{1}{4}\) ĐKXĐ:x ≠ -2
⇒ 4(2x+3) = 2x+4
⇔ 8x+12 = 2x+4
⇔ 8x - 2x = 4 - 12
⇔ 6x = 8
⇔ x = \(\frac{4}{3}\) (TMĐKXĐ)
Vậy để H = \(\frac{1}{4}\) thì x = \(\frac{4}{3}\)