Đáp án:
1.
a, `ĐKXĐ : x ne ± 6 ; x ne 0`
b, Ta có
`P = (x/(x^2 - 36) - (x - 6)/(x^2 + 6x)) : (2x - 6)/(x^2 + 6x)`
`= (x/[(x - 6)(x + 6)] - (x - 6)/[x(x + 6)]) : (2x - 6)/[x(x + 6)]`
`= (x^2/[x(x - 6)(x + 6)] - (x - 6)^2/[x(x - 6)(x + 6)] ) : [(2x - 6)(x - 6)]/[x(x - 6)(x + 6)]`
`= (x^2 - (x - 6)^2)/[x(x - 6)(x + 6)] . [x(x - 6)(x + 6)]/[(2x - 6)(x - 6)]`
`= [(x + x - 6)(x - x + 6)]/[x(x - 6)(x + 6)] . [x(x - 6)(x + 6)]/[(2x - 6)(x - 6)]`
`= [6(2x - 6)]/[x(x - 6)(x + 6)] . [x(x - 6)(x + 6)]/[(2x - 6)(x - 6)]`
`= [6(2x - 6)x(x - 6)(x + 6)]/[x(x - 6)(x + 6)(2x - 6)(x - 6)]`
`= 6/(x - 6)`
c, Để `P < 0`
`<=> 6/(x - 6) < 0`
`<=> x - 6 < 0`
`<=> x < 6`
Vậy `x < 6 , x ne 0 , x ne -6` thì `P < 0`
2.
a, `ĐKXĐ : x ne 0 ; x ne -5`
b, Ta có
`A = (x^2 + 2x)/(2x + 10) + (x - 5)/x + (50 - 5x)/[2x(x + 5)]`
`= (x^2 + 2x)/[2(x + 5)] + (x - 5)/x + (50 - 5x)/[2x(x + 5)]`
`= [x(x^2 + 2x)]/[2x(x + 5)] + [2(x + 5)(x - 5)]/[2x(x + 5)] + (50 - 5x)/[2x(x + 5)]`
`= (x^3 + 2x^2 + 2x^2 - 50 + 50 - 5x)/[2x(x + 5)]`
`= (x^3 + 4x^2 - 5x)/[2x(x + 5)]`
`= [x(x + 5)(x - 1)]/[2x(x + 5)]`
`= (x - 1)/2`
c, Để `A = 1`
`<=> (x - 1)/2 = 1`
`<=> x - 1 = 2`
`<=> x = 3`
Giải thích các bước giải:
