\(a,P=\left(\dfrac{2x-1}{x+3}-\dfrac{x}{3-x}-\dfrac{3-10x}{x^2-9}\right):\dfrac{x+2}{x-3}\left(x\ne\pm3;x\ne-2\right)\\ P=\dfrac{2x^2-7x+3+x^2+3x-3+10x}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x-3}{x+2}\\ P=\dfrac{3x^2+6x}{\left(x-3\right)\left(x+2\right)}=\dfrac{3x\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}=\dfrac{3x}{x-3}\\ b,x^2-7x+12=0\\ \Leftrightarrow\left(x-3\right)\left(x-4\right)=0\\ \Leftrightarrow x=4\left(x\ne3\right)\\ \Leftrightarrow A=\dfrac{3\cdot4}{4-3}=12\\ c,P=\dfrac{3\left(x-3\right)+9}{x-3}=3+\dfrac{9}{x-3}\in Z\\ \Leftrightarrow x-3\inƯ\left(9\right)=\left\{-9;-3;-1;1;3;9\right\}\\ \Leftrightarrow x\in\left\{-6;0;2;4;6;12\right\}\)

Bài 11: 

Ta có: \(x=\dfrac{-101}{a+7}\) nguyên khi \(-101⋮a+7\)

Vậy: \(a+7\inƯ\left(101\right)\)

\(Ư\left(101\right)=\left\{101;1;-101;-1\right\}\)

\(a+7\in\left\{101;1;-101;-1\right\}\)

\(\Rightarrow a\in\left\{94;-108;-6;-8\right\}\)

Vậy x sẽ nguyên khi \(a\in\left\{94;-108l-6;-8\right\}\)

Bài 12:

Ta có: \(t=\dfrac{3x+8}{x-5}=\dfrac{3x+15-7}{x-5}=\dfrac{3\left(x+5\right)-7}{x-5}=3+\dfrac{7}{x-5}\)

t nguyên khi \(\dfrac{7}{x+5}\) nguyên tức là \(x-5\inƯ\left(7\right)\) 

\(Ư\left(7\right)=\left\{-7;7;-1;1\right\}\)

\(\Rightarrow x-5\in\left\{-7;7;-1;1\right\}\)

\(\Rightarrow x\in\left\{12;-2;4;6\right\}\)

Vậy t sẽ nguyên khi \(x\in\left\{12;-2;4;6\right\}\)

a: =>-2x=90/91

hay x=-45/91

b: =>2x=-7

hay x=-7/2

c: ->-3x=-12

hay x=4

Bài 1: 

a: =>2x-9=10/91

=>2x=829/91

hay x=829/182

b: =>2x=-7

hay x=-7/2

c: =>-3x=-12

hay x=4

1: Để A nguyên thì x+3-4 chia hết cho x+3

=>\(x+3\in\left\{1;-1;2;-2;4;-4\right\}\)

=>\(x\in\left\{-2;-4;-1;-5;1;-7\right\}\)

2: Để B nguyên thì 2x+4-9 chia hết cho x+2

=>\(x+2\in\left\{1;-1;3;-3;9;-9\right\}\)

=>\(x\in\left\{-1;-3;1;-5;7;-11\right\}\)