Bài 1

\(\frac{2017}{2018}+\frac{2018}{2019}\)và \(\left(\frac{2017+2018}{2018+2019}\right)\)mk chữa lại đề luôn đó 

Ta tách :

\(\frac{2017}{\left(2018+2019\right)+2018}\)

đến đây ta tách 

\(\frac{2017}{2018+2019}< \frac{2017}{2018}\)

vậy....

mấy câu khác tương tự 

2) \(\frac{\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}}{\frac{2}{2003}+\frac{2}{2004}+\frac{2}{2005}}\)

= \(\frac{\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}}{2.\frac{1}{2003}+2.\frac{1}{2004}+2.\frac{1}{2005}}\)

=\(\frac{1\left(\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}\right)}{2.\left(\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}\right)}\)

= \(\frac{1}{2}\)

3) \(2013+\left(\frac{2013}{1+2}\right)+\left(\frac{2013}{1+2+3}\right)+...+\left(\frac{2013}{1+2+3+...+2012}\right)\)

= \(2013.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2012}\right)\)

= \(2013.\left(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{2025078}\right)\)

= \(2013.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{4050156}\right)\)

=\(4026.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2012.2013}\right)\)

= \(4026.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2012}-\frac{1}{2013}\right)\)

= \(4026.\left(1-\frac{1}{2013}\right)\)

= \(4026.\frac{2012}{2013}\)

=\(4024\)

= ( 1 + 2 + 3 + 4 +.....+ 99 ) x (2013 x ( 3 - 2 ) - 2-13 )

= ( 1 + 2 + 3 + 4 +......+ 99 ) x ( 2013  - 2013 )

= ( 1 + 2 + 3 + 4 +....+ 99 ) x 0

= 0

\(a,\Leftrightarrow3\left(x+3\right)=0\Leftrightarrow x=-3\\ b,\Leftrightarrow\left(x^2-2\right)\left(6x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2=2\\6x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\\x=-\dfrac{1}{6}\end{matrix}\right.\\ c,\Leftrightarrow\left(x-2013\right)\left(4x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2013\\x=\dfrac{1}{4}\end{matrix}\right.\\ d,\Leftrightarrow\left(x+1\right)^2-\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x+1-1\right)=0\\ \Leftrightarrow x\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)

bài 1

3 /x+3/ = x(x+3)

<=> 3x + 9 = x^2 + 3x hoặc -3x -9 = x^2 + 3x

với 3x + 9 = x^2 + 3x

=> 9 = x^2

=> x = 3 và x = -3

với -3x - 9 = x^2 + 3x

=> -9 = x^2 ( vô lí)

vậy x= 3 hoặc x= -3

a) Ta có: \(2\sqrt{3}=\sqrt{4\cdot3}=\sqrt{12}\)

\(3\sqrt{2}=\sqrt{9\cdot2}=\sqrt{18}\)

mà \(\sqrt{12}< \sqrt{18}\)(vì 12<18)

nên \(2\sqrt{3}< 3\sqrt{2}\)

b) Ta có: \(\left(2\sqrt{3}+1\right)^2=8+4\sqrt{3}+1=9+4\sqrt{3}\)

\(4^2=16=9+7\)

mà \(4\sqrt{3}< 7\left(\sqrt{48}< \sqrt{49}\right)\)

nên \(\left(2\sqrt{3}+1\right)^2< 4^2\)

hay \(2\sqrt{3}+1< 4\)

c) Ta có: \(\sqrt{2015}-\sqrt{2014}=\dfrac{1}{\sqrt{2015}+\sqrt{2014}}\)

\(\sqrt{2014}-\sqrt{2013}=\dfrac{1}{\sqrt{2014}+\sqrt{2013}}\)

Ta có: \(\sqrt{2015}+\sqrt{2014}>\sqrt{2013}+\sqrt{2014}\)

\(\Leftrightarrow\dfrac{1}{\sqrt{2015}+\sqrt{2014}}< \dfrac{1}{\sqrt{2013}+\sqrt{2014}}\)

hay \(\sqrt{2015}-\sqrt{2014}< \sqrt{2014}-\sqrt{2013}\)

\(a\))Ta có:\(2\sqrt{3}=\sqrt{12}\)

             \(3\sqrt{2}=\sqrt{18}\)

Vì \(\sqrt{12}< \sqrt{18}\)

⇒\(2\sqrt{3}< 3\sqrt{2}\)

\(b\))Ta có:\(2\sqrt{3}+1=\sqrt{12}+1\)

             \(4=3+1=\sqrt{9}+1\)

Vì \(\sqrt{12}+1>\sqrt{9}+1\)

⇒\(2\sqrt{3}+1>4\)