a) \(A=\left(\dfrac{x}{x+3}-\dfrac{2}{x-3}+\dfrac{x^2-1}{9-x^2}\right):\left(2-\dfrac{x+5}{x+3}\right)\) (ĐK: \(x\ne\pm3\))

\(A=\left[\dfrac{x\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{2\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{x^2-1}{\left(x+3\right)\left(x-3\right)}\right]:\left(2+\dfrac{x+5}{x+3}\right)\)

\(A=\dfrac{x^2-3x-2x-6-x^2+1}{\left(x+3\right)\left(x-3\right)}:\dfrac{2\left(x+3\right)-\left(x+5\right)}{x+3}\)

\(A=\dfrac{-5x-5}{\left(x+3\right)\left(x-3\right)}\cdot\dfrac{x+3}{x+1}\)

\(A=\dfrac{-5\left(x+1\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)\left(x+1\right)}\)

\(A=\dfrac{-5}{x-3}\)

b) Ta có: \(\left|x\right|=1\)

TH1: \(\left|x\right|=-x\) với \(x< 0\)

Pt trở thành:

\(-x=1\) (ĐK: \(x< 0\)) 

\(\Leftrightarrow x=-1\left(tm\right)\)

Thay \(x=-1\) vào A ta có:

\(A=\dfrac{-5}{x-3}=\dfrac{-5}{-1-3}=\dfrac{5}{4}\)

TH2: \(\left|x\right|=x\) với \(x\ge0\)

Pt trở thành:

\(x=1\left(tm\right)\) (ĐK: \(x\ge0\)) 

Thay \(x=1\) vào A ta có:

\(A=\dfrac{-5}{x-3}=\dfrac{-5}{1-2}=\dfrac{5}{2}\)

c) \(A=\dfrac{1}{2}\) khi:

\(\dfrac{-5}{x-3}=\dfrac{1}{2}\)

\(\Leftrightarrow-10=x-3\)

\(\Leftrightarrow x=-10+3\)

\(\Leftrightarrow x=-7\left(tm\right)\)

d) \(A\) nguyên khi:

\(\dfrac{-5}{x-3}\) nguyên

\(\Rightarrow x-3\inƯ\left(-5\right)\)

\(\Rightarrow x\in\left\{8;-2;2;4\right\}\)

a: \(A=\left(\dfrac{x}{x+3}-\dfrac{2}{x-3}+\dfrac{x^2-1}{9-x^2}\right):\left(2-\dfrac{x+5}{x+3}\right)\)

\(=\dfrac{x\left(x-3\right)-2\left(x+3\right)-x^2+1}{\left(x-3\right)\left(x+3\right)}:\dfrac{2x+6-x-5}{x+3}\)

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

\(=\dfrac{-5x-5}{\left(x-3\right)}\cdot\dfrac{1}{x+1}=\dfrac{-5}{x-3}\)

b: |x|=1

=>x=-1(loại) hoặc x=1(nhận)

Khi x=1 thì \(A=\dfrac{-5}{1-3}=-\dfrac{5}{-2}=\dfrac{5}{2}\)

c: A=1/2

=>x-3=-10

=>x=-7

d: A nguyên

=>-5 chia hết cho x-3

=>x-3 thuộc {1;-1;5;-5}

=>x thuộc {4;2;8;-2}

\(\left(x+4\right)^2-81=0\Leftrightarrow\left(x+4\right)^2-9^2=0\)

\(\Leftrightarrow\left(x+4+9\right)\times\left(x+4-9\right)=0\)

\(\Leftrightarrow\left(x+13\right)\times\left(x-5\right)=0\)

\(\left[{}\begin{matrix}x+13=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-13\\x=5\end{matrix}\right.\)

Bài 2:

a, |x-1| -x +1=0

|x-1| = 0-1+x

|x-1| = -1 + x

 \(\orbr{\begin{cases}x-1=-1+x\\x-1=1-x\end{cases}}\)

 \(\orbr{\begin{cases}x=-1+x+1\\x=1-x+1\end{cases}}\)

 \(\orbr{\begin{cases}x=x\\x=2-x\end{cases}}\)

x = 2-x

2x = 2

x = 2:2

x=1

b, |2-x| -2 = x

|2-x| = x+2

\(\orbr{\begin{cases}2-x=x+2\\2-x=2-x\end{cases}}\)

2-x = x+2

x+x = 2-2

2x = 0

x = 0

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=>5x+25=0

=>5x=-25

hay x=-5

mjk ko bik giải câu a có dc  ko

b) A=\(\frac{5x-2}{x-3}=\frac{5x-15+13}{x-3}=\frac{5x-15}{x-3}+\frac{13}{x-3}=\frac{5\left(x-3\right)}{x-3}+\frac{13}{x-3}=5+\frac{13}{x-3}\)

Để A thuộc Z thì \(5+\frac{13}{x-3}\in Z\)

=>13 chia hết cho x-3

=>x-3 \(\in\)Ư(13)={-1;1;-13;13}

x-3=-1           x-3=1            x-3 =-13           x-3=13

x  =-1+3        x   =1+3        x    =-13+3        x   =13+3

x=2               x  =4              x=-10              x=16

Vậy x=2;4;-10;16 thì A thuộc Z

c)B=\(\frac{6x-1}{3x+2}=\frac{6x+4-5}{3x+2}=\frac{6x+4}{3x+2}+\frac{-5}{3x+2}=\frac{2\left(3x+2\right)}{3x+2}+\frac{-5}{3x+2}=2+\frac{-5}{3x+2}\)

Để B thuộc Z thì \(2+\frac{-5}{3x+2}\in Z\)

=>-5 chia hết cho 3x+2

=>3x+2\(\in\)Ư(-5)={-1;1;-5;5}

3x+2=-1             3x+2=1              3x+2=-5           3x+2=5

3x    =-3             3x    =-1             3x   =-7            3x    =3

x       =-1             x     =-1/3            x   =-7/3          x     =1

Vậy x=-1;-1/3;-7/3;1 thì B thuộc Z

d) C=\(\frac{10x}{5x-2}=\frac{10x-4+4}{5x-2}=\frac{10-4}{5x-2}+\frac{4}{5x-2}=\frac{2\left(5x-2\right)}{5x-2}+\frac{4}{5x-2}=2+\frac{4}{5x-2}\)

Để C thuộc Z thì \(2+\frac{4}{5x-2}\in Z\)

=> 4 chia hết cho 5x-2

=>5x-2\(\in\)Ư(4)={-1;1;-2;2;-4;4}

5x-2=-1           5x-2=1             5x-2=2          5x-2=-2           5x-2=4            5x-2=-4

bạn tự giải tìm x như các bài trên nhé

d) bạn ghi đề mjk ko hjeu

e)E=\(\frac{4x+5}{x-3}=\frac{4x-12+17}{x-3}=\frac{4x-12}{x-3}+\frac{17}{x-3}=\frac{4\left(x-3\right)}{x-3}+\frac{17}{x-3}=4+\frac{17}{x-3}\)

Để E thuộc Z thì\(4+\frac{17}{x-3}\in Z\)

=>17 chia hết cho x-3

=>x-3 \(\in\)Ư(17)={1;-1;17;-17}

x-3=1       x-3=-1            x-3=17           x-3=-17

bạn tự giải tìm x nhé

điều cuối cùng cho mjk ****

a) x - \(\frac{1}{9}\)= \(\frac{8}{3}\)

    x       = \(\frac{8}{3}\)+ \(\frac{1}{9}\)

    x       = \(\frac{24}{9}+\frac{1}{9}\)

    x       = \(\frac{25}{9}\)

tick cho mình nha! please!!!

x-1 phần 9 mà ko phải x trừ 1 phần 9

\(\frac{x-1}{9}=\frac{8}{3}\)

\(\Rightarrow\left(x-1\right)\cdot3=8\cdot9\)

\(\Rightarrow3x-3=72\)

\(\Rightarrow3x=75\)

\(\Rightarrow x=25\)

BÀI 3 : 

Để \(A=\frac{3n-5}{n+4}\)là giá trị nguyên 

\(\Rightarrow3n-5⋮n+4\)

\(\Rightarrow3n+12-17⋮n+4\)

\(\Rightarrow3\left(n+4\right)-17⋮n+4\)

\(\Rightarrow n+4\inƯ\left(17\right)=\left\{\pm1;\pm17\right\}\)

\(\Rightarrow n\in\left\{-3;-5;18;-10\right\}\)