mn giúp em với :( cảm ơn ạ

Đáp án+ Giải thích các bước giải:

  `a,`

`Q = {12x-45}/{x^2 -7x +12} - {x+5}/{x-4} + {2x +3}/{3-x}`
`ĐKXĐ: x \ne 4;3`

`Q = {12x -45}/{x^2 -3x -4x +12} - {x+5}/{x-4} + {2x +3}/{3 - x}`
`Q = {12x -45}/{x(x-3) -4(x-3)} - {x+5}/{x-4} - {2x +3}/{x -3}`
`Q = {12x -45}/{(x-3)(x-4)} - {(x+5)(x-3)}/{(x-3)(x-4)} - {(2x +3)(x-4)}/{(x-4)(x-3)}`

`Q = {12x - 45 - (x^2 -3x +5x -15) -(2x^2 -8x +3x -12)}/{(x-4)(x-3)}`
`Q = {12x - 45 - x^2 -2x + 15 - 2x^2 +5x + 12}/{(x-4)(x-3)}`
`Q = {-3x^2 + 15x -18}/{(x-4)(x-3)}`
`Q = {-3x^2 +6x +9x -18}/{(x-4)(x-3)}`
`Q = {-3x(x -2) +9(x-2)}/{(x-4)(x-3)}`
`Q = {-3(x-3)(x-2)}/{(x-4)(x-3)}`
`Q = {-3(x-2)}/{x-4}`
`b,`

`|x| = 3`

\(\left[ \begin{array}{l}x=3(ktm)\\x=-3(tm)\end{array} \right.\)

`Thay: x = -3`. Ta có:

`Q = {-3(-3-2)}/{-3-4}`
`Q = - {17}/7`
`c,`

`{-3(x-2)}/{x-4}`
`= {-3(x-4 +2)}/{x-4}`
`= {-3(x-4) -6}/{x-4}`

`= {-3(x-4)}/{x-4} - 6/{x-4}`
`= -3 - 6/{x-4}`
`Q \in ZZ <=> -3 - 6/{x-4} \in ZZ`
`=> 6/{x-4} \in ZZ`
`=> x - 4 \in {+-1; +- 2; +-3; +-6}`

\begin{array}{|c|c|c|}\hline \text{$x-4$}&\text{-1}&\text{1}&\text{-2}&\text{2}&\text{-3}&\text{3}&\text{-6}&\text{6}\\\hline \text{$x$}&\text{3(ktm)}&\text{5(tm)}&\text{2(tm)}&\text{6(tm)}&\text{1(tm)}&\text{7(tm)}&\text{-2(tm)}&\text{10(tm)}\\\hline\end{array}

`=> x \in {5; 2; 6; 1;7 -2; 10}`