\(a,\frac{3x^3+6x^2}{x^3+2x^2+x+2}=\frac{3x^2\left(x+2\right)}{x^2\left(x+2\right)+\left(x+2\right)}\)

\(=\frac{3x^2\left(x+2\right)}{\left(x+2\right)\left(x^2+1\right)}\)

\(\RightarrowĐKXĐ:x\ne-2\)

\(b,\) Với \(x\ne-2\) thì :

\(\frac{3x^3+6x^2}{x^3+2x^2+x+2}=\frac{3x^2\left(x+2\right)}{\left(x+2\right)\left(x^2+1\right)}\)

\(=\frac{3x^2}{x^2+1}\)

Vì \(3x^2,\left(x^2+1\right)\ge0vs\forall x\)

\(\Rightarrow\frac{3x^2}{x^2+1}\ge0\)

Do đó : Giá trị của phân thức luôn không âm khi nó được xác định.

a) ĐKXĐ: \(^{x^3+2x^2+x+2}\)khác 0

=> x^2(x+2)+(x+2) Khác 0

=> (x^2+1)(x+2) khác 0

=> x^2 khác -1(vô lý) và x khác -2

Vậy x khác -2 thì biểu thức A được xác định

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

\(=\frac{3x^2\left(x+2\right)}{\left(x^2+1\right)\left(x+2\right)}=\frac{3x^2}{x^2+1}\)

Để A=2 thì \(\frac{3x^2}{x+2}=2\)=>\(3x^2=2\left(x^2+1\right)=>3x^2=2x^2+2\)

\(=>x^2=2=>x=\sqrt{2}\)(Thỏa mãn điều kiện xác định)

1.a)\(\frac{x^3}{x^2-4}-\frac{x}{x-2}-\frac{2}{x+2}\)

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

Để biểu thức được xác định thì:\(\left(x+2\right)\left(x-2\right)\ne0\)\(\Rightarrow x\ne\pm2\)

                                                      \(\left(x+2\right)\ne0\Rightarrow x\ne-2\)

                                                      \(\left(x-2\right)\ne0\Rightarrow x\ne2\)

                         Vậy để biểu thức xác định thì : \(x\ne\pm2\)

b) để C=0 thì ....

1, c , bn Nguyễn Hữu Triết chưa lm xong 

ta có : \(/x-5/=2\)

\(\Rightarrow\orbr{\begin{cases}x-5=2\\x-5=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=7\\x=3\end{cases}}\)

thay x = 7  vào biểu thứcC

\(\Rightarrow C=\frac{4.7^2\left(2-7\right)}{\left(7-3\right)\left(2+7\right)}=\frac{-988}{36}=\frac{-247}{9}\)KL :>...

thay x = 3 vào C 

\(\Rightarrow C=\frac{4.3^2\left(2-3\right)}{\left(3-3\right)\left(3+7\right)}\)

=> ko tìm đc giá trị C tại x = 3

chết mk nhìn nhầm phần c bài 2 :

\(2,\left(\frac{2+x}{2-x}+\frac{4x^2}{x^2-4}-\frac{2-x}{2+x}\right):\frac{x^2-3x}{2x^2-x^3}\)

Để P xác định 

\(\Rightarrow2-x\ne0\Rightarrow x\ne2\)

\(2+x\ne0\Rightarrow x\ne-2\)

\(x^2-4\ne0\Rightarrow x\ne0\)

\(x^2-3x\ne0\Rightarrow x\ne3\)

b, \(P=\left(\frac{2+x}{2-x}+\frac{4x^2}{\left(2+x\right)\left(2-x\right)}+\frac{2-x}{2+x}\right):\frac{x\left(x-3\right)}{x^2\left(2-x\right)}\)

\(P=\left[\frac{4+4x+x^2}{\left(2-x\right)\left(2+x\right)}-\frac{4x^2}{\left(2+x\right)\left(2-x\right)}-\frac{4-4x+x^2}{\left(2+x\right)\left(2-x\right)}\right].\frac{x\left(2-x\right)}{x-3}\)

\(P=\left[\frac{8x-4x^2}{\left(2-x\right)\left(2+x\right)}\right].\frac{x\left(2-x\right)}{x-3}=\frac{4x\left(2-x\right)}{\left(2-x\right)\left(2+x\right)}.\frac{x\left(2-x\right)}{x-3}\)

\(P=\frac{4x^2\left(2-x\right)}{\left(x-3\right)\left(2+x\right)}\)

d, ĐỂ \(p=\frac{8x^2-4x^3}{x^2-x-6}< 0\)

\(TH1:8x^2-4x^3< 0\)

\(\Rightarrow8x^2< 4x^3\)

\(\Rightarrow2< x\Rightarrow x>2\)

\(TH2:x^2-x-6< 0\Rightarrow x^2< x+6\)

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c) tự làm, đkxđ: x≠1;x≠−1

ê k bn với mk ik

😘 😘 😘 😘

a/. ĐKXĐ : (x-1)(x+1) # 0 => x # 1 hay x # -1

b/. \(B=\left[\frac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}+\frac{3.2}{2\left(x-1\right)\left(x+1\right)}-\frac{\left(x+3\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}\right].\frac{4\left(x-1\right)\left(x+1\right)}{5}\)

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

\(B=\frac{2\left(4-2x\right)}{5}\)

Em xem lại đè nhé. Đề như vậy thì sẽ ko rút gọn đc hết x trên tử. nên B vẫn phụ thuộc vào biến x. 

chao cac bạn và a chi nếu đề sửa lai vây thi minh làm thế nào ( x+1/2x-2 + 3/x^2+1 - x+3/2x+1 )* (4x^2 -1)/5

\(\frac{x+3}{2x+2}\)

sẽ ra đó bạn

a/ A=\(\frac{x\left(3x-1\right)}{\left(3x-1\right)^2}=\frac{x}{3x-1}\)

A xác định khi 3x-1 #0 <=> x khác 1/3

b/ x=8 => A=\(\frac{8}{3.8-1}=\frac{8}{23}\)

c/ A\(\le0\)Khi:

+/\(\hept{\begin{cases}x\ge0\\3x-1\le0\end{cases}}< =>0\le x\le\frac{1}{3}\)

+/ \(\hept{\begin{cases}x\le0\\3x-1\ge0\end{cases}}\)Không có giá trị x phù hợp

Vậy để A<0 <=> \(0\le x\le\frac{1}{3}\)

a,\(\frac{3x^2-x}{9x^2-6x+1}=\frac{x\left(3x-1\right)}{\left(3x-1\right)^2}=\frac{x}{3x-1}\)

Vậy đk xác định của phân thức là \(x\ne\frac{1}{3}\)

b, Ta thay x=8

\(\frac{x}{3x-1}=\frac{8}{3.8-1}=\frac{8}{23}\)

c, x<0

\(\Rightarrow\frac{x}{3x-1}=-1\Leftrightarrow x=0,25\)

mấy bạn kia dùng dấu \("\le"\) là sai nhé 

\(c)\) \(\frac{3x^2-x}{9x^2-6x+1}=\frac{x\left(3x-1\right)}{\left(3x-1\right)^2}=\frac{x}{3x-1}< 0\)

TH1 : \(\hept{\begin{cases}x< 0\\3x-1>0\end{cases}\Leftrightarrow\hept{\begin{cases}x< 0\\x>\frac{1}{3}\end{cases}}}\) ( loại ) 

TH2 : \(\hept{\begin{cases}x>0\\3x-1< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x>0\\x< \frac{1}{3}\end{cases}}\Leftrightarrow0< x< \frac{1}{3}}\)

Vậy để phân thức âm thì \(0< x< \frac{1}{3}\)

PS : giải thích dùm 1 người, ko copy