Đáp án:
a, `ĐKXĐ P(x) : x ne ± 2`
`Q(x) : x ne 2`
Ta có
`P = (x + 2)/(2x- 4) + (x - 2)/(2x + 4) + -8/(x^2 - 4)`
`= (x + 2)/[2(x - 2)] + (x - 2)/[2(x + 2)] + -8/[(x - 2)(x + 2)]`
`= (x + 2)^2/[2(x - 2)(x + 2)] + (x - 2)^2/[2(x - 2)(x + 2)] + -16/[2(x - 2)(x + 2)]`
`= (x^2 + 4x + 4 + x^2 - 4x + 4 - 16)/[2(x - 2)(x + 2)] `
`= (2x^2 - 8)/[2(x - 2)(x + 2)]`
`= [2(x - 2)(x + 2)]/[2(x - 2)(x + 2)] `
`= 1`
b, `P(x) : Q(x)`
`= 1 : 4/(x - 2)`
`= (x - 2)/4`
c, Để `P(x) : Q(x) = 1`
`<=> (x - 2)/4 = 1`
`<=> x- 2 = 4`
`<=> x = 6`
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