Đáp án + Giải thích các bước giải:
`d) (8 - x)/(x - 7) - 8 = 1/(x - 7) (x ne7) <=> (8 - x)/(x - 7) - [8(x - 7)]/(x - 7) = 1/(x - 7)` $\\$ `<=> [8 - x - 8(x - 7)]/(x - 7) = 1/(x - 7)` $\\$ `<=> 8 - x - 8(x - 7) = 1 <=> 8 - x - 8x + 56 = 1` $\\$ `<=> 64 - 9x = 1 <=> 9x = 63 <=> x = 7(loại)`
Vậy `S = emptyset`
`e) (x + 5)/(x - 5) - (x - 5)/(x + 5) = 20/(x^2 - 25) (x ne pm 5)` $\\$ `<=> (x + 5)/(x- 5) - (x - 5)/(x + 5) = 20/[(x - 5)(x + 5)] ` $\\$ `<=> [(x + 5)(x + 5)]/[(x - 5)(x + 5)] - [(x - 5)(x - 5)]/[(x - 5)(x + 5)] = 20/[(x - 5)(x + 5)]` $\\$ `<=> [(x + 5)(x + 5) - (x - 5)(x - 5)]/[(x - 5)(x + 5)] = 20/[(x - 5)(x+ 5)]` $\\$ `<=> (x + 5)(x + 5) - (x - 5)(x - 5) = 20` $\\$ `<=> x^2 + 5x + 5x + 25 - (x^2 - 5x - 5x + 25) = 20` $\\$ `<=> x^2 + 5x + 5x + 25 - x^2 + 5x + 5x - 25 = 20` $\\$ `<=> 20x = 20 <=> x = 1(tm)`
Vậy S = {1}
`f) 1/(x -1) + 2/(x + 1) = x/(x^2 - 1) (x ne pm 1)` $\\$ `<=> [1(x + 1)]/[(x - 1)(x + 1)] + [2(x - 1)]/[(x - 1)(x + 1)] = x/[(x - 1)(x + 1)]` $\\$ `<=> [1(x + 1) + 2(x - 1)]/[(x - 1)(x + 1)] = x/[(x - 1)(x + 1)]` $\\$ `<=> 1(x + 1) + 2(x - 1) = x` $\\$ `<=> x + 1 + 2x - 2 - x = 0` $\\$ ` <=> 2x-1 = 0 <=> x = 1/2(tm)`
Vậy `S = {1/2}`
`g) x/[2(x - 3)] + x/[2(x + 1)] = (2x)/[(x + 1)(x - 3)] (x ne -1,x ne 3)` $\\$ `<=> [x(x + 1)]/[2(x + 1)(x - 3)] + [x(x - 3)]/[2(x + 1)(x - 3)] = (2x*2)/[2(x + 1)(x - 3)]` $\\$ `<=> [x(x + 1) + x(x - 3)]/[2(x + 1)(x - 3)] = (4x)/[2(x + 1)(x + 3)]` $\\$ `<=> x(x + 1) + x(x - 3) = 4x <=> x^2 + x + x^2 - 3x = 4x` $\\$ `<=> x^2 + x^2 + x - 3x - 4x = 0 <=> 2x^2 - 6x = 0 ` $\\$ `<=> 2x(x - 3) = 0 <=> `\(\left[ \begin{array}{l}x=0(tm)\\x=3(loại)\end{array} \right.\)
Vậy S = {0}
`h) 5 + 76/(x^2 - 16) = (2x - 1)/(x + 4) - (3x - 1)/(4 - x) (x ne pm 4) ` $\\$ `<=> 5 + 76/[(x - 4)(x + 4)] = (2x - 1)/(x + 4) - [-(3x - 1)]/(x - 4)` $\\$ `<=> 5 + 76/[(x - 4)(x + 4)] = (2x - 1)/(x + 4) - (1 - 3x)/(x - 4)` $\\$ `<=> 5 + 76/[(x - 4)(x + 4)] = [(2x - 1)(x - 4)]/[(x - 4)(x + 4)] - [(1 - 3x)(x + 4)]/[(x - 4)(x + 4)` $\\$ `<=> [5(x - 4)(x + 4)]/[(x - 4)(x + 4)] + 76/[(x - 4)(x + 4)] = [(2x - 1)(x - 4)]/[(x - 4)(x + 4)] - [(1 - 3x)(x + 4)]/[(x - 4)(x + 4)]` $\\$ `<=> 5(x - 4)(x + 4) + 76 = (2x - 1)(x - 4) - (1 - 3x)(x + 4)` $\\$ `<=> 5(x^2 - 16) + 76 = 2x^2 - 8x - x + 4 - (x + 4 - 3x^2 - 12x)` $\\$ `<=> 5x^2 - 80 + 76 = 2x^2 - 8x - x + 4 - x - 4 + 3x^2 + 12x ` $\\$ `<=> 5x^2 - 80 + 76 - 2x^2 + 8x + x - 4 + x + 4 - 3x^2 - 12x = 0` $\\$ `<=> -4 - 2x = 0 <=> 2x = -4 <=> x = -2`
Vậy S = {-2}
`i) 90/x - 36/(x - 6) = 2 ( x ne 0 , x ne 6) <=> [90(x - 6)]/[x(x - 6)] - (36x)/[x(x - 6)] = [2*x(x - 6)]/[x(x - 6)` $\\$ `<=> 90(x - 6) - 36x = 2x(x - 6)` $\\$ `<=> 90x - 540 - 36x = 2x^2 - 12x` $\\$ `<=> 90x - 36x + 12x = 2x^2 + 540` $\\$ `<=> 66x = 2x^2 + 540` $\\$ `<=> 2(x^2 + 270) = 66x` $\\$ `<=> x^2 + 270 = 33x` $\\$ `<=> x^2 - 33x + 270 = 0` $\\$ `<=> x^2 - 15x - 18x + 270 = 0` $\\$ `<=> x(x - 15) - 18(x - 15) = 0` $\\$ `<=> (x - 15)(x - 18) = 0` `<=>`\(\left[ \begin{array}{l}x=15\\x=18\end{array} \right.\) `(tm)`
Vậy S = {15,18}
`k) 1/x + 1/(x + 10) = 1/12 (x ne 0,x ne -10) <=> (x + 10 + x)/[x(x + 10)] = 1/12` $\\$ `<=> (2x + 10)/[x(x + 10)] = 1/12 <=> x(x + 10) = 12(2x + 10)` $\\$ `<=> x^2 + 10x = 24x + 120 <=> x^2 + 10x - 24x - 120 = 0` $\\$ `<=> x^2 - 14x - 120 = 0 <=> x^2 + 6x - 20x - 120 = 0` $\\$ `<=> x(x + 6) - 20(x + 6) = 0` $\\$ `<=> (x + 6)(x - 20) = 0` `<=>` \(\left[ \begin{array}{l}x=-6\\x=20\end{array} \right.\) `(tm)`
Vậy S = {-6;20}
`l) (x + 3)/(x - 3) - 1/x = 3/[x(x - 3)] <=> [(x + 3).x - 1(x - 3)]/[x(x - 3)] = 3/[x(x - 3)` $\\$ `<=> x(x + 3) - 1(x - 3) = 3` $\\$ `<=> x^2 + 3x - x + 3 = 3 <=> x^2 + 2x = 0 <=> x(x + 2) = 0 ` $\\$ `<=> ` \(\left[ \begin{array}{l}x=0(loại)\\x=-2(tm)\end{array} \right.\)
Vậy S = {-2}
`m) 3 /(x + 2) - 2/(x - 2) + 8/(x^2 - 4) = 0 (x ne pm 2)` $\\$ `<=> [3(x - 2) - 2(x + 2)]/[(x - 2)(x + 2)] + 8/[(x - 2)(x + 2)] = 0` $\\$ `<=> 3(x - 2) - 2(x + 2) + 8 = 0` $\\$ `<=> 3x - 6 - 2x - 4 + 8 = 0` $\\$ `<=> x - 2 = 0 <=> x = 2(loại)`
Vậy `S = emptyset`
`n) 3/(x + 2) - 2/(x - 3) = 8/[(x - 3)(x + 2)] ( x ne 3 , x ne -2)` $\\$ `<=> [3(x - 3) - 2(x + 2)]/[(x - 3)(x + 2)]= 8/[(x - 3)(x + 2)]` $\\$ `<=> 3(x - 3) - 2(x + 2) = 8` $\\$ `<=> 3x - 9 - 2x - 4 = 8` $\\$ ` <=> x - 9 - 4 - 8 = 0` $\\$ `<=> x - 21 = 0 <=> x = 21(tm)`
Vậy S = {21}
