a) \(ĐKXĐ:\hept{\begin{cases}x\ne2\\x\ne3\end{cases}}\)

\(A=\frac{2x-12}{x^2-5x+6}-\frac{x+3}{x-2}+\frac{2x}{x-3}\)

\(\Leftrightarrow A=\frac{2x-12-x^2+9+2x^2-4x}{\left(x-2\right)\left(x-3\right)}\)

\(\Leftrightarrow A=\frac{x^2-2x-3}{\left(x-2\right)\left(x-3\right)}\)

\(\Leftrightarrow A=\frac{\left(x-3\right)\left(x+1\right)}{\left(x-2\right)\left(x-3\right)}\)

\(\Leftrightarrow A=\frac{x+1}{x-2}\)

b) Thay \(x=5\)vào A ta được :

\(A=\frac{5+1}{5-2}=2\)

c) Để \(A\inℤ\)

\(\Leftrightarrow x+1⋮x-2\)

\(\Leftrightarrow3⋮x-2\)

\(\Leftrightarrow x-2\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

\(\Leftrightarrow x\in\left\{1;3;-1;5\right\}\)

Vì \(x\ne3\)

Vậy để \(A\inℤ\Leftrightarrow x\in\left\{1;-1;5\right\}\)

Bạn xem lại đề !

a, ĐKXĐ: \(x\ne\pm3\)

\(A=\frac{x\left(x-3\right)+2x\left(x+3\right)-3x^2-12}{\left(x-3\right)\left(x+3\right)}.\frac{x-3}{3}\)

\(=\frac{3x-12}{\left(x-3\right)\left(x+3\right)}.\frac{x-3}{3}=\frac{3x-12}{3x+9}\)

b, \(x=-4\Rightarrow A=\frac{3.\left(-4\right)-12}{3.\left(-4\right)+9}=8\)

c, \(A\in Z\Rightarrow3x-12⋮\left(3x+9\right)\Rightarrow3x+9-21⋮\left(3x+9\right)\Rightarrow21⋮\left(3x+9\right)\)

\(\Rightarrow3x+9\inƯ\left(21\right)=\left\{\pm1;\pm3;\pm7;\pm21\right\}\)

Mà \(3x+9⋮3\Rightarrow3x+9\in\left\{-21;-3;3;21\right\}\Rightarrow x\in\left\{-10;-4;-2;4\right\}\) (thỏa mãn điều kiện)

a, ĐỂ A xác định : 

\(\Rightarrow\hept{\begin{cases}x+3\ne0\\x-3\ne0\\x^2-9\ne0\end{cases}}\Rightarrow x\ne\pm3.\)

\(A=\left(\frac{x}{x+3}+\frac{2x}{x-3}-\frac{3x^2+12}{\left(x+3\right)\left(x-3\right)}\right):\frac{3}{x-3}\)

\(A=\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{2x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{3x^2+12}{\left(x-3\right)\left(x+3\right)}:\frac{3}{x-3}\)

\(A=\frac{x^2-3x+2x^2+6x-3x^2+12}{\left(x-3\right)\left(x+3\right)}.\frac{x-3}{3}\)

\(A=\frac{3x+12}{\left(x-3\right)\left(x+3\right)}.\frac{x-3}{3}\)

\(A=\frac{x-4}{x+3}\)

b

a: \(B=\dfrac{3x\left(2x-3\right)-4\left(2x+3\right)-4x^2+23x+12}{\left(2x-3\right)\left(2x+3\right)}\cdot\dfrac{2x+3}{x+3}\)

\(=\dfrac{6x^2-9x-8x-12-4x^2+23x+12}{2x-3}\cdot\dfrac{1}{x+3}\)

\(=\dfrac{2x^2+6x}{\left(2x-3\right)}\cdot\dfrac{1}{x+3}=\dfrac{2x}{2x-3}\)

b: 2x^2+7x+3=0

=>(2x+3)(x+2)=0

=>x=-3/2(loại) hoặc x=-2(nhận)

Khi x=-2 thì \(A=\dfrac{2\cdot\left(-2\right)}{-2-3}=\dfrac{-4}{-7}=\dfrac{4}{7}\)

d: |B|<1

=>B>-1 và B<1

=>B+1>0 và B-1<0

=>\(\left\{{}\begin{matrix}\dfrac{2x+2x-3}{2x-3}>0\\\dfrac{2x-2x+3}{2x-3}< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-3< 0\\\dfrac{4x-3}{2x-3}>0\end{matrix}\right.\Leftrightarrow x< \dfrac{3}{4}\)

CẢM ƠN BẠN NHA

a. \(P=\left(\frac{x^2+2x}{x^3+2x^2+5x+10}+\frac{4}{x^2+5}\right)\)\(.\frac{x^2+5}{x+1}\)

   \(P=\left(\frac{x\left(x+2\right)}{\left(x+2\right)\left(x^2+5\right)}+\frac{4}{x^2+5}\right)\)\(.\frac{x^2+5}{x+1}\)

  \(P=\left(\frac{x}{x^2+5}+\frac{4}{x^2+5}\right)\)\(.\frac{x^2+5}{x+1}\)

\(P=\frac{x+4}{x^2+5}.\frac{x^2+5}{x+1}\)\(=\frac{x+4}{x+1}\)

phần b em tự giải nhé chị chỉ giải đc đến đây  thôi

 a)  P = (\(\frac{x\cdot\left(x+2\right)}{\left(x^2+5\right)\cdot\left(x+2\right)}+\frac{4}{x^2+5}\))*\(\frac{x^2+5}{x+1}\)=\(\frac{x+4}{x^2+5}\cdot\frac{x^2+5}{x+1}\)=\(\frac{x+4}{x+1}\) (ĐKXĐ: x\(x=\left\{-2;-1\right\}\)

b) TA CÓ : P= \(\frac{x+4}{x+1}=1+\frac{3}{x+1}\forall x\ne\left\{-2;-1\right\}\) . VẬY P \(\inℤ\) KHI \(\frac{3}{X+1}\) \(ℤ\in\) \(\Rightarrow x+1\)LÀ ƯỚC CỦA 3 \(\Rightarrow x=+1=\left\{-3;-1;1;3\right\}\Rightarrow x=\left\{-4;0;2\right\}\)

* x=-2 thì P=-4 (NHÂN),x=-1 thì P KO  XÁC ĐỊNH

a) ĐKXĐ: \(x\notin\left\{0;3;1\right\}\)

Sửa đề: \(A=\left(\dfrac{x-3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\right):\dfrac{2x-2}{x}\)

Ta có: \(A=\left(\dfrac{x-3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\right):\dfrac{2x-2}{x}\)

\(=\dfrac{x^2-6x+9-x^2+9}{x\left(x-3\right)}\cdot\dfrac{x}{2\left(x-1\right)}\)

\(=\dfrac{-6x+18}{x\left(x-3\right)}\cdot\dfrac{x}{2\left(x-1\right)}\)

\(=\dfrac{-6\left(x-3\right)}{x\left(x-3\right)}\cdot\dfrac{x}{2\left(x-1\right)}\)

\(=\dfrac{-3}{x-1}\)

b) Để A nguyên thì \(-3⋮x-1\)

\(\Leftrightarrow x-1\in\left\{1;-1;3;-3\right\}\)

\(\Leftrightarrow x\in\left\{2;0;4;-2\right\}\)

Kết hợp ĐKXĐ, ta được: \(x\in\left\{2;-2;4\right\}\)