K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

a) \(p=\left(\frac{x^2-x}{x+1}\right)\left(\frac{4x-2x+2}{x\left(x-1\right)}\right)\)

\(=\frac{x\left(x-1\right)}{x+1}.\frac{2\left(x+1\right)}{x\left(x-1\right)}=2\)

b)\(m=\frac{x+2-\left(x-2\right)+x^2+4x}{\left(x-2\right)\left(x+2\right)}=\frac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{x+2}{x-2}=1+\frac{4}{x-2}\)

Để m nguyên thì \(4⋮x-2\)

\(\Rightarrow x-2\in\left\{1,2,4,-1,-2,-4\right\}\)

\(\Leftrightarrow x\in\left\{3,4,6,1,0,-2\right\}\)

8 tháng 3 2020

\(M=\frac{1}{x-2}-\frac{1}{x+2}+\frac{x^2+4x}{x^2-4}\left(x\ne\pm2\right)\)

\(\Leftrightarrow M=\frac{x+2}{\left(x-2\right)\left(x+2\right)}-\frac{x-2}{\left(x+2\right)\left(x-2\right)}+\frac{x^2+4x}{\left(x-2\right)\left(x+2\right)}\)

\(\Leftrightarrow M=\frac{x+2-x+2+x^2+4x}{\left(x-2\right)\left(x+2\right)}\)

\(\Leftrightarrow M=\frac{x^2+4x+4}{\left(x-2\right)\left(x+2\right)}=\frac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}=\frac{x+2}{x-2}\)

Để M có giá trị nguyên thì x+2 chia hết cho x-2

Ta có x+2=x-2+4

=> x-2+4 chia hết cho x-2

=>4 chia hết cho x-2

Vì x nguyên => x-2 nguyên

=> x-2 thuộc Ư (4)={-4;-2;-1;1;2;4}

Ta có bảng

x-2-4-2-1124
x-201346
5 tháng 6 2019

a.

\(ĐKXĐ:x\ne\pm1;\)

Ta có:

\(P=\left(\frac{x^4+x^2-4x+1}{x^2-1}-\frac{x-1}{x+1}+\frac{x+1}{x-1}\right)\cdot\frac{x\left(x+1\right)-\left(1+x\right)}{x^3-1}\)

\(\Rightarrow P=\left(\frac{x^4+x^2-4x+1}{x^2-1}-\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}+\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}\right)\cdot\frac{\left(x+1\right)\left(x-1\right)}{x^3-1}\)

\(\Rightarrow P=\left(\frac{x^4+x^2-4x+1}{x^2-1}-\frac{x^2-2x+1}{x^2-1}+\frac{x^2+2x+1}{x^2-1}\right)\cdot\frac{x^2-1}{x^3-1}\)

\(\Rightarrow P=\frac{x^4+x^2+1}{x^2-1}\cdot\frac{x^2-1}{x^3-1}\)

\(\Rightarrow P=\frac{x^4+x^2+1}{x^3-1}\)

b.

Để P là số nguyên thì  \(x^4+x^2+1⋮x^3-1\)

\(\Rightarrow\left(x^4-x\right)+\left(x^2+x+1\right)⋮\left(x-1\right)\left(x^2+x+1\right)\)

\(\Rightarrow x\left(x^3-1\right)+\left(x^2+x+1\right)⋮\left(x-1\right)\left(x^2+x+1\right)\)

\(\Rightarrow x\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)⋮\left(x-1\right)\left(x^2+x+1\right)\)

\(\Rightarrow\left(x^2+x+1\right)\left(x^2-x+1\right)⋮\left(x-1\right)\left(x^2+x+1\right)\)

\(\Rightarrow x^2-x+1⋮x-1\)

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

\(\Rightarrow1⋮x-1\)

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

\(\Rightarrow x=1\left(KTMĐK\right);x=0\)

Vậy x=0.

P/S:Không chắc chắn lắm đâu nha mn,nếu có j sai thì ib vs em ah.

12 tháng 6 2018

a) Đk \(x\ne\pm1\), sau khi rút gọn ta được: (bạn tư làm)

   \(P=\frac{x}{x+1}\)

b) Khi \(\left|x-\frac{2}{3}\right|=\frac{1}{3}\) thì hoặc \(x-\frac{2}{3}=\frac{1}{3}\) hoặc \(x-\frac{2}{3}=-\frac{1}{3}\)

Hay là \(x=1\) hoặc \(x=\frac{1}{3}\)

Do để P có nghĩa thì \(x\ne\pm1\) nên \(x=\frac{1}{3}\), khi đó: 

 \(P=\frac{\frac{1}{3}}{\frac{1}{3}+1}=\frac{1}{4}\)

c) P > 1 khi \(\frac{x}{x+1}>1\)

   \(\Leftrightarrow1-\frac{1}{x+1}>1\)

   \(\Leftrightarrow\frac{1}{x+1}< 0\)

   \(\Leftrightarrow x< -1\)

e) Đề không rõ ràng

1 tháng 5 2021

dễ mà ko bt lm à

10 tháng 4 2019

\(A=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{8}{x^2-1}\right):\left(\frac{1}{x-1}-\frac{7x+3}{1-x^2}\right)\)

\(A=\left[\frac{x^2+2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{x^2-2x+1}{\left(x+1\right)\left(x-1\right)}+\frac{8}{\left(x+1\right)\left(x-1\right)}\right]:\left[\frac{x+1}{\left(x+1\right)\left(x-1\right)}-\frac{3-7x}{\left(x+1\right)\left(x-1\right)}\right]\)

\(A=\left[\frac{x^2+2x+1-x^2+2x-1+8}{\left(x+1\right)\left(x-1\right)}\right]:\frac{x+1-3+7x}{\left(x+1\right)\left(x-1\right)}\)

\(A=\frac{4x+8}{\left(x+1\right)\left(x-1\right)}.\frac{\left(x+1\right)\left(x-1\right)}{8x-2}\)

...................... 

10 tháng 4 2019

tìm giá trị x nguyên để A nguyên đi

10 tháng 2 2021

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

\(=\frac{-\left(x+2\right)^2\left(x-2\right)\left(x+1\right)}{x\left(x+2\right)}=\frac{-\left(x\pm2\right)\left(x+1\right)}{x}\)

c, Theo bài ra ta có : \(C=\frac{A}{B}\)hay \(\frac{\frac{-\left(x\pm2\right)\left(x+1\right)}{x}}{\frac{4}{\left(x-2\right)^2}}=\frac{\frac{-\left(x+2\right)\left(x+1\right)}{x}}{\frac{4}{x-2}}\)

d, Theo bài ra ta có : 

\(C>0\)hay \(\frac{\frac{-\left(x+2\right)\left(x+1\right)}{x}}{\frac{4}{x-2}}>0\)

\(\Leftrightarrow\frac{-\left(x+2\right)\left(x+1\right)}{x}.\frac{x-2}{4}>0\)

\(\Leftrightarrow-\left(x+2\right)\left(x+1\right)>0\Leftrightarrow\left(x+2\right)\left(x+1\right)>0\)

\(\Leftrightarrow x>-2;x>-1\Rightarrow x>-1\)