a) x=1

vì 11*2.1chia hết cho 2.1-1

a ) x=2 

b ) x =9 

y = 12

2.\(P=\frac{x+1}{2x+5}+\frac{x+2}{2x+4}+\frac{x+3}{2x+3}\)

        \(=\frac{x+1}{2x+5}+1+\frac{x+2}{2x+4}+1+\frac{x+3}{2x+3}+1-3\)

          \(=\frac{3x+6}{2x+5}+\frac{3x+6}{2x+4}+\frac{3x+6}{2x+3}-3\)

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

Áp dụng BĐT Cô-si ta có:

\(a+b+c\ge3\sqrt[3]{abc}\)

\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge3\sqrt[3]{\frac{1}{abc}}\)

Nhân vế với vế của 3 BĐT trên ta được:

\(\left(a+b+c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge3\sqrt[3]{abc}.3\sqrt[3]{\frac{1}{abc}}=9\)

\(\Leftrightarrow\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge\frac{9}{a+b+c}\left(1\right)\)

Áp dụng BĐT \(\left(1\right)\)ta được:

\(\frac{1}{2x+5}+\frac{1}{2x+4}+\frac{1}{2x+3}\ge\frac{9}{6x+12}\)

\(\Leftrightarrow\left(3x+6\right)\left(\frac{1}{2x+5}+\frac{1}{2x+4}+\frac{1}{2x+3}\right)-3\ge3\left(x+2\right).\frac{9}{6\left(x+2\right)}-3\)

\(\Leftrightarrow P\ge\frac{3}{2}\left(đpcm\right)\)

Bài1

a. x=1/4+-2/13; x/-3=-2/3+1/7; x=7/-25+1/5

x = 1/4 + (-2/13)

x = 1/4 - 2/13

x = 13/52 - 8/52

x = 5/52

Vậy x = 5/52

x/-3 = -2/3 + 1/7

x/-3 = - 14/21 + 3/21

x/-3 = - 11/21

x = - 11/21 x (-3)

x = 11/7

Vậy x = 11/7

x=7/-25+1/5

x = - 7/25 + 5/25

x = - 2/25

Vậy x = - 2/25

Bài 1:

b. x=5/11+4/-9;5 /9+x/-1=-1/3; x+7/12=7/18-1/8

x = 5/11 + 4/-9

x = 5/11 - 4/9

x = 45/99 - 44/99

x = 1/99

Vậy x = 1/99

5 /9+x/-1=-1/3

x/-1 = - 1/3 - 5/9

-x = - 3/9 - 5/9

- x = - 8/9

x = - 8/9 : (-1)

x = 8/9

Vậy x = 8/9

x+7/12=7/18-1/8

x + 7/12 = 28/72 - 9/72

x + 7/12 = 19/72

x = 19/72 - 7/12

x = - 23/72

Vậy x = - 23/72

a: \(P=\left(\dfrac{-\left(x+3\right)}{x-3}+\dfrac{x-3}{x+3}+\dfrac{4x^2}{x^2-9}\right):\dfrac{2x+1-x-3}{x+3}\)

\(=\dfrac{-x^2-6x-9+x^2-6x+9+4x^2}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x+3}{x-2}\)

\(=\dfrac{4x^2-12x}{x-3}\cdot\dfrac{1}{x-2}=\dfrac{4x}{x-2}\)

b: \(2x^2-5x+2=0\)

=>(x-2)(2x-1)=0

=>x=1/2

Thay x=1/2 vào P, ta được:

\(P=\left(4\cdot\dfrac{1}{2}\right):\left(\dfrac{1}{2}-2\right)=2:\dfrac{-3}{2}=\dfrac{-4}{3}\)