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14 tháng 5 2018

\(\dfrac{x-3}{2014}+\dfrac{x-2}{2015}=\dfrac{x-2015}{2}+\dfrac{x-2014}{3}\)

\(\dfrac{x-3}{2014}-1+\dfrac{x-2}{2015}-1=\dfrac{x-2015}{2}-1+\dfrac{x-2014}{3}-1\)

\(\dfrac{x-2017}{2014}+\dfrac{x-2017}{2015}=\dfrac{x-2017}{2}+\dfrac{x-2017}{3}\)

\(\left(x-2017\right)\)\(\left(\dfrac{1}{2014}+\dfrac{1}{2015}-\dfrac{1}{2}-\dfrac{1}{3}\right)=0\)

Do : \(\dfrac{1}{2014}< \dfrac{1}{2015}< \dfrac{1}{2}< \dfrac{1}{3}\)

\(\dfrac{1}{2014}+\dfrac{1}{2015}-\dfrac{1}{2}-\dfrac{1}{3}< 0\)

⇔ x - 2017 = 0

⇔ x = 2017

KL....

9 tháng 3 2020

gõ phân số ra cho mk nhìn đc ko cậu

Sửa đề: \(\dfrac{x+2}{2014}+\dfrac{x+1}{2015}=\dfrac{x+2001}{15}+\dfrac{x+2014}{2}\)
Ta có: \(\dfrac{x+2}{2014}+\dfrac{x+1}{2015}=\dfrac{x+2001}{15}+\dfrac{x+2014}{2}\)

\(\Leftrightarrow\dfrac{x+2}{2014}+1+\dfrac{x+1}{2015}+1=\dfrac{x+2001}{15}+1+\dfrac{x+2014}{2}+1\)

\(\Leftrightarrow\dfrac{x+2016}{2014}+\dfrac{x+2016}{2015}=\dfrac{x+2016}{15}+\dfrac{x+2016}{2}\)

\(\Leftrightarrow\dfrac{x+2016}{2014}+\dfrac{x+2016}{2015}-\dfrac{x+2016}{15}-\dfrac{x+2016}{2}=0\)

\(\Leftrightarrow\left(x+2016\right)\left(\dfrac{1}{2014}+\dfrac{1}{2015}-\dfrac{1}{15}-\dfrac{1}{2}\right)=0\)

mà \(\dfrac{1}{2014}+\dfrac{1}{2015}-\dfrac{1}{15}-\dfrac{1}{2}\ne0\)

nên x+2016=0

hay x=-2016

Vậy: S={-2016}

\(\dfrac{x-2014}{4}+\dfrac{x-2015}{3}=\dfrac{x-13}{2005}+\dfrac{x-14}{2004}\)

<=>\(\left(\dfrac{x-2014}{4}-1\right)+\left(\dfrac{x-2015}{3}-1\right)=\left(\dfrac{x-13}{2005}-1\right)+\left(\dfrac{x-14}{2004}-1\right)\)

<=>\(\dfrac{x-2018}{4}+\dfrac{x-2018}{3}=\dfrac{x-2018}{2005}+\dfrac{x-2018}{2004}\)

<=>\(\left(x-2018\right).\left[\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{2005}-\dfrac{1}{2004}\right]=0\)

<=>  \(x-2018=0\)

=>x=2018

Vậy S= {2018}

Chúc bạn học tốt!
#Yuii

29 tháng 4 2021

hahathank

28 tháng 2 2016

x=-2,500620501

3 tháng 3 2016

x = 2014 => x + 1 = 2015

=> f(2014) = x2014 - (x + 1).x2013 + (x + 1).x2012 - ... - (x + 1).x + x + 1

= x2014 - x2014 - x2013 + x2013 + x2012 - ... - x2 - x + x + 1

= 1

3 tháng 3 2016

minh moi hoc lop 5

7 tháng 5 2017

\(\dfrac{x-5}{2012}+\dfrac{x-4}{2013}=\dfrac{x-3}{2014}+\dfrac{x-2}{2015}\)

\(\Rightarrow\left(\dfrac{x-5}{2012}-1\right)+\left(\dfrac{x-4}{2013}-1\right)=\left(\dfrac{x-3}{2014}-1\right)+\left(\dfrac{x-2}{2015}-1\right)\)

\(\Leftrightarrow\dfrac{x-2017}{2012}+\dfrac{x-2017}{2013}=\dfrac{x-2017}{2014}+\dfrac{x-2017}{2015}\)

\(\Leftrightarrow\dfrac{x-2017}{2012}+\dfrac{x-2017}{2013}-\dfrac{x-2017}{2014}-\dfrac{x-2017}{2015}=0\)

\(\Leftrightarrow\left(x-2017\right)\left(\dfrac{1}{2012}+\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\right)=0\)

\(\Rightarrow x-2017=0\Leftrightarrow x=2017\)

Vậy x = 2017

7 tháng 5 2017

cảm ơn nhé

(x-1)/2015 + x/2014 + 1/503 - (x-3)/2013 - x/2012 - 1/1007 =0

(x-2016)/2015  + (x-2016)/2014 - (x-2016)/2012 - (x-2016)/2013 = 0

(x-2016) ( 1/2015 + 1/2016 - 1/2013 - 1/2012) = 0

Mà 1/2015 + 1/2016 - 1/2013 - 1/2012 khác 0

Suy ra x -2016=0

x=2016

Chỗ nào thắc mắc nhớ hỏi mik nhe!

27 tháng 2 2020

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