Tập hợp các giá trị x thõa mãn \(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
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TN
2 tháng 10 2016
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\Leftrightarrow\frac{x+1}{2015}+1+\frac{x+2}{2014}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)
\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
\(\Leftrightarrow x+2016=0\).Do \(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\ne0\)
\(\Leftrightarrow x=-2016\)
HT
7 tháng 9 2016
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\Leftrightarrow\)\(\frac{x+1}{2015}+1+\frac{x+2}{2014}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\)
\(\Leftrightarrow\)\(\frac{x+1}{2015}+\frac{2015}{2015}+\frac{x+20}{2014}+\frac{2014}{2014}=\frac{x+3}{2013}+\frac{2013}{2013}+\frac{x+4}{2012}+\frac{2012}{2012}\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\Leftrightarrow\)\(\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)
\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
Suy ra \(x+2016=0\) \(\Leftrightarrow x=-2016\)
Vậy \(x\in\left\{-2016\right\}\)
MB
7 tháng 9 2016
bạn cộng thêm 1 vào mỗi phân thức đó
sau đó sẽ có phân tử chung là x+2016
kết quả là x=-2016
10 tháng 10 2016
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\Leftrightarrow\frac{x+1}{2015}+1+\frac{x+2}{2014}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)
\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
\(\Leftrightarrow x+2016=0\).Do \(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\ne0\)
\(\Leftrightarrow x=-2016\)
29 tháng 12 2015
2) xét tử ta có
2014+2013/2+2012/3+...+2/2013+1/2014
=(1+2013/2)+(1+2012/3)+...+(1+2/2013)+(1+1/2014)+1
=2015/2+2015/3+...+2015/2013+2015/2014+2015/2015
=2015(1/2+1/3+...+1/2013+1/2014+1/2015) (1)
mà mẫu bằng 1/2+1/3+1/4+...+1/2014+1/2015 (2)
từ (1),(2)=> phân thức trên =2015
DP
1
NH
12 tháng 9 2016
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\left(\frac{x+1}{2015}+1\right)+\left(\frac{x+2}{2014}+1\right)=\left(\frac{x+3}{2013}+1\right)+\left(\frac{x+4}{2012}+1\right)\)
\(\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\left(x+2016\right).\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
\(x+2016=0\)
\(x=-2016\)
MA
17 tháng 9 2016
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\Leftrightarrow\frac{x+1}{2015}+1+\frac{x+2}{2014}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)
\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
Có: \(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\ne0\)
\(\Rightarrow x+2016=0\)
\(\Rightarrow x=-2016\)
N
2
BN
3
CC
11 tháng 2 2020
\(\frac{x}{2012}+\frac{x-1}{2013}+\frac{x-2}{2014}-\frac{x-3}{2015}=\frac{x-4}{1008}\)
\(\Leftrightarrow\left(\frac{x}{2012}+1\right)+\left(\frac{x-1}{2013}+1\right)+\left(\frac{x-2}{2014}+1\right)-\left(\frac{x-3}{2015}+1\right)=\frac{x-4}{1008}+2\)
\(\Leftrightarrow\frac{x+2012}{2012}+\frac{x+2012}{2013}+\frac{x+2012}{2014}-\frac{x+2012}{2015}=\frac{x-4+1008.2}{1008}\)
\(\Leftrightarrow\frac{x+2012}{2012}+\frac{x+2012}{2013}+\frac{x+2012}{2014}-\frac{x+2012}{2015}=\frac{x+2012}{1008}\)
\(\Leftrightarrow\frac{x+2012}{2012}+\frac{x+2012}{2013}+\frac{x+2012}{2014}-\frac{x+2012}{2015}-\frac{x+2012}{1008}=0\)
\(\Leftrightarrow\left(x+2012\right)\left(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{1008}\right)=0\)
Vì \(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{1008}\ne0\)
\(\Rightarrow x+2012=0\)\(\Leftrightarrow x=-2012\)
Vậy \(x=-2012\)
K
1
11 tháng 11 2016
=\(\left(\frac{x-1}{2015}-1\right)+\left(\frac{x-2}{2014}-1\right)-\left(\frac{x-3}{2013}-1\right)-\left(\frac{x-4}{2012}-1\right)\)
=\(\frac{x-2016}{2015}+\frac{x-2016}{2014}-\frac{x-2106}{2013}-\frac{x-2016}{2012}\)
=\(\left(x-2016\right).\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)\)
Mà: \(\frac{1}{2012}>\frac{1}{2015}\) và \(\frac{1}{2014}< \frac{1}{2013}\)
=>\(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\) khác \(0\)
Nên: \(x-2016=0\)
=>\(x=2016\)
