\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)

\(\Leftrightarrow2+\frac{x+4}{2000}+\frac{x+3}{2001}=2+\frac{x+2}{2002}+\frac{x+1}{2003}\)

\(\Leftrightarrow\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2001}+1\right)\)

\(\Leftrightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)

\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)

Mà \(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\ne0\)

Suy ra x+2004=0

\(\Leftrightarrow x=-2004\)

Answer:

a) \(\frac{5x}{2x+2}+1=\frac{6}{x+1}\)

\(\Rightarrow\frac{5x}{2\left(x+1\right)}+\frac{2\left(x+1\right)}{2\left(x+1\right)}=\frac{12}{2\left(x+1\right)}\)

\(\Rightarrow5x+2x+2-12=0\)

\(\Rightarrow7x-10=0\)

\(\Rightarrow x=\frac{10}{7}\)

b) \(\frac{x^2-6}{x}=x+\frac{3}{2}\left(ĐK:x\ne0\right)\)

\(\Rightarrow x^2-6=x^2+\frac{3}{2}x\)

\(\Rightarrow\frac{3}{2}x=-6\)

\(\Rightarrow x=-4\)

c) \(\frac{3x-2}{4}\ge\frac{3x+3}{6}\)

\(\Rightarrow\frac{3\left(3x-2\right)-2\left(3x+3\right)}{12}\ge0\)

\(\Rightarrow9x-6-6x-6\ge0\)

\(\Rightarrow3x-12\ge0\)

\(\Rightarrow x\ge4\)

d) \(\left(x+1\right)^2< \left(x-1\right)^2\)

\(\Rightarrow x^2+2x+1< x^2-2x+1\)

\(\Rightarrow4x< 0\)

\(\Rightarrow x< 0\)

e) \(\frac{2x-3}{35}+\frac{x\left(x-2\right)}{7}\le\frac{x^2}{7}-\frac{2x-3}{5}\)

\(\Rightarrow\frac{2x-3+5\left(x^2-2x\right)}{35}\le\frac{5x^2-7\left(2x-3\right)}{35}\)

\(\Rightarrow2x-3+5x^2-10x\le5x^2-14x+21\)

\(\Rightarrow6x\le24\)

\(\Rightarrow x\le4\)

f) \(\frac{3x-2}{4}\le\frac{3x+3}{6}\)

\(\Rightarrow\frac{3\left(3x-2\right)-2\left(3x+3\right)}{12}\le0\)

\(\Rightarrow9x-6-6x-6\le0\)

\(\Rightarrow3x\le12\)

\(\Rightarrow x\le4\)

Ta có: A = \(\frac{3n+2}{n-5}=\frac{3\left(n-5\right)+17}{n-5}=3+\frac{17}{n-5}\)

Để A thuộc Z thì 17 \(⋮\)n - 5 => n - 5 \(\in\)Ư(17) = {1; -1; 17; -17}

Lập bảng :

Vậy n thuộc {6;4;22;-12} thì A thuộc Z

A=(3n-15)+17/n-5

A=3+ 17/n-5

A thuoc Z thi 3 + 17/n-5 thuoc Z -->17/n-5 thuoc Z

-->n-5 thuoc Ư(17)

11/6>5/4 : 2/5>7/25

Bán kính hình tròn là:

\(5,8:2=2,9\left(dm\right)\)

Diện tích hình tròn là:

\(2,9\times2,9\times3,14=26,4047\left(dm^2\right)=26,41\left(dm^2\right)\)

Đáp số:...

26,41 dm vuông là đúng nha bn Trần Văn Hùng

a. \(\frac{2}{5}+\frac{3}{5}:\left(\frac{3}{5}+\frac{-2}{3}\right)-3\frac{1}{2}\)

\(=\frac{2}{5}+\frac{3}{5}:\frac{-1}{15}-\frac{7}{2}\)

\(=\frac{2}{5}+\left(-9\right)-\frac{7}{2}\)

\(=-\frac{43}{5}-\frac{7}{2}\)

\(=-\frac{121}{10}\)

\(a)\frac{2}{5}+\frac{3}{5}:\left(\frac{3}{5}+\frac{-2}{3}\right)-3\frac{1}{2}\)

\(=\frac{2}{5}+\frac{3}{5}:\frac{-1}{15}-\frac{7}{2}\)

\(=\frac{2}{5}+(-9)-\frac{7}{2}\)

\(=-\frac{43}{5}-\frac{7}{2}=-\frac{121}{10}\)

bn ghi đề bài rõ đi,mik ko hiểu

cho mình xin lỗi nhé