`a,`

\(x^2-3x\ne0\)

`<=>x(x-3)`\(\ne0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x-3\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne3\end{matrix}\right.\)

`b,`

đặt `A=(x^2-6x+9)/(x^2-3x)`

`A= ((x-3)^2)/(x(x-3))`

`A= (x-3)/x`

`c, `

để `x=5`

`=> A= (x -3)/x=(5-3)/5= 2/5`

a/ ĐKXĐ: \(x^2-3x\ne0\) \(\Leftrightarrow\) x\(\ne\)0,x\(\ne\)3

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

c/ x= 5 => \(\dfrac{x-3}{x}=\dfrac{5-3}{5}=\dfrac{2}{5}\)

Answer:

a. \(ĐKXĐ:x^2-9\ne0\Rightarrow x^2\ne9\Rightarrow x\ne\pm3\)

b. \(A=\frac{x^2-6x+9}{x^2-9}=\frac{\left(x-3\right)^2}{\left(x-3\right).\left(x+3\right)}=\frac{x-3}{x+3}\)

c. \(A=7\)

\(\Rightarrow\frac{x-3}{x+3}=7\)

\(\Rightarrow x-3=7.\left(x+3\right)\)

\(\Rightarrow x-3=7x+21\)

\(\Rightarrow x-3-7x-21=0\)

\(\Rightarrow-6x-24=0\)

\(\Rightarrow x=-4\)

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)

a ĐKXĐ: x<>0; x<>3

b: Sửa đề; x^2-6x+9/x^2-3x

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

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

a: ĐKXĐ: x<>-3

b: =x+3

\(P=\dfrac{3x^2+6x+3}{x+1}\)

\(a,\) Điều kiện xác định: \(x+1\ne0\Leftrightarrow x\ne-1\)

\(b,P=\dfrac{3x^2+6x+3}{x+1}=\dfrac{3\left(x^2+2x+1\right)}{x+1}=\dfrac{3\left(x+1\right)^2}{x+1}=3\left(x+1\right)=3x+3\)

\(c,x=1\Rightarrow P=3.1+3=6\)

a) điều kiện xác định: x≠3 và x≠2

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

Tại x=13 ta có \(\dfrac{13+2}{13-3}\)=\(\dfrac{3}{2}\)

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