a: ĐKXĐ: a<>3; a<>-3; a<>-1

b: \(P=\dfrac{2a^2-3a+3a+9-2a^2-3}{\left(a-3\right)\left(a+3\right)}\cdot\dfrac{a-3}{a+1}\)

\(=\dfrac{6}{\left(a+3\right)\left(a+1\right)}\)

c: |a|=2

=>a=2 hoặc a=-2

Khi a=-2 thì \(P=\dfrac{6}{\left(-2+3\right)\left(-2+1\right)}=-6\)

Khi a=2 thì \(P=\dfrac{6}{\left(2+3\right)\left(2+1\right)}=\dfrac{6}{5\cdot3}=\dfrac{2}{5}\)

a) ĐK: \(x\ne4,x\ne2;x\ne-2\)

b) \(A=\dfrac{x^3}{x-4}-\dfrac{x}{x-2}-\dfrac{2}{x+2}\)

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

\(A=\dfrac{x^3-x^2-2x-2x+4}{\left(x+2\right)\left(x-2\right)}\)

\(A=\dfrac{x^3-x^2-4x+4}{\left(x+2\right)\left(x-2\right)}\)

\(A=\dfrac{x^2\left(x-1\right)-4\left(x-1\right)}{\left(x+2\right)\left(x-2\right)}\)

\(A=\dfrac{\left(x-1\right)\left(x^2-4\right)}{x^2-4}\)

\(A=x-1\)

c) \(A=0\) khi:

\(x-1=0\)

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

d) A dương khi: \(A>0\)

\(x-1>0\)

\(\Leftrightarrow x>1\)

Kết hợp với đk: 

\(x>1,x\ne4,x\ne2\)

a) Biểu thức A xác định `<=>x^2-1 ne 0 <=> (x-1)(x+1) ne 0 <=> x ne +-1`

b) `A=(x^2-3x-4)/(x^2 -1) = (x^2+x-4x-4)/(x^2-1) = (x(x+1)-4(x+1))/(x^2-1)`

`= ((x+1)(x-4))/((x+1)(x-1))=(x-4)/(x-1)`

c) `A` là số nguyên `<=> (x-4) vdots\ (x-1)`

`<=>[(x-1)-3] vdots\ (x-1)`

`<=> -3\ vdots\ (x-1)`

`<=> (x-1)\ in\ Ư(-3)`

`<=>(x-1)\ in\ {-3;-1;3;1}`

`<=>x\ in\ {-2;0;4;2}`

Vậy...

a: ĐKXĐ: x<>1; x<>-1

b: \(A=\dfrac{\left(x-4\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x-4}{x-1}\)

c: Để A là số nguyên thì x-1-3 chia hết cho x-1

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

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

\(a,ĐK:x^2-1\ne0\)

\(\Rightarrow\left(x-1\right)\left(x+1\right)\ne0\)

\(\Rightarrow\left[{}\begin{matrix}x-1\ne0\\x+1\ne0\end{matrix}\right.\)           \(\Rightarrow\left[{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)

       Vậy ĐKXĐ của \(x\) là \(x\ne\pm1\)

\(b,\dfrac{x^2-3x-4}{x^2-1}=\dfrac{\left(x-4\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x-4}{x-1}\)

\(c,\) Ta có: \(\dfrac{x-4}{x-1}=\dfrac{x-1-3}{x-1}=\dfrac{x-1}{x-1}-\dfrac{3}{x-1}=1-\dfrac{3}{x-1}\)

Để \(A\in Z\) thì \(\dfrac{3}{x-1}\in Z\)

\(\Rightarrow x-1\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

Ta có bảng sau:

Vậy \(x\in\left\{2;0;4;-2\right\}\)

a) A đc xác định <=>2x+4\(\left\{{}\begin{matrix}2x+4\ne0\\x^2-4\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-2\\x\ne2\end{matrix}\right.\)

câu b bn quy đòng mẫu là đc

a) ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

b) Ta có: \(A=\dfrac{x}{2x+4}+\dfrac{3x+2}{x^2-4}\)

\(=\dfrac{x}{2\left(x+2\right)}+\dfrac{3x+2}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{x\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}+\dfrac{2\left(3x+2\right)}{2\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{x^2-2x+6x+4}{2\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{x^2+4x+4}{2\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{\left(x+2\right)^2}{2\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{x+2}{2\left(x-2\right)}\)

c) Để A=0 thì \(\dfrac{x+2}{2\left(x-2\right)}=0\)

\(\Leftrightarrow x+2=0\)

hay x=-2(Không thỏa mãn ĐKXĐ)

Vậy: Không có giá trị nào của x để A=0

a) ĐKXĐ: \(x\ne\pm1\)

b) \(A=\dfrac{x^3-1}{x^2-1}\cdot\left(\dfrac{1}{x-1}-\dfrac{x+1}{x^2+x+1}\right)\left(dkxd:x\ne\pm1\right)\)

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

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

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

\(=\dfrac{x+2}{x^2-1}\)

c) Có: \(\left|x+3\right|=1\Leftrightarrow\left[{}\begin{matrix}x+3=1\\x+3=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-4\end{matrix}\right.\left(tmdk\right)\)

+) Với \(x=-2\), thay vào \(A\), ta được:

\(A=\dfrac{-2+2}{\left(-2\right)^2-1}=0\)

+) Với \(x=-4\), thay vào \(A\), ta được:

\(A=\dfrac{-4+2}{\left(-4\right)^2-1}=-\dfrac{2}{15}\)

\(\text{#}Toru\)

a) Phân thức A được xác định khi: \(x^2-1\ne0\Rightarrow\left(x-1\right)\left(x+1\right)\ne0\Rightarrow\left\{{}\begin{matrix}x+1\ne0\\x-1\ne0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)

Vây ĐKXĐ của A là \(\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)

b)Ta có: \(A=\dfrac{x^2+2x+1}{x^2-1}=\dfrac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}=\dfrac{\left(x+1\right)}{\left(x-1\right)}\)

Vậy \(A=\dfrac{x+1}{x-1}\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)

c) Ta có A=2 <-> \(\dfrac{x+1}{x-1}=2\Leftrightarrow x+1=2\left(x-1\right)\Leftrightarrow x+1=2x-2\)

\(\Leftrightarrow x+1-2x+2=0\Leftrightarrow3-x=0\Rightarrow x=3\)

Vậy khi x=3 thì A=2

\(a,ĐK:x\ne\pm2\\ b,A=\dfrac{5x+10+14x-28-20}{2\left(x-2\right)\left(x+2\right)}=\dfrac{19\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}=\dfrac{19}{2\left(x+2\right)}\\ c,x=-\dfrac{1}{2}\Leftrightarrow A=\dfrac{19}{2\left(2-\dfrac{1}{2}\right)}=\dfrac{19}{2\cdot\dfrac{3}{2}}=\dfrac{19}{3}\)

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

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

c: Thay x=2 vào A, ta được:

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

d: Để A=2 thì x+1=2x-2

=>-x=-3

hay x=3(nhận)