\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\)

\(\Leftrightarrow\frac{x+1}{2015}+1+\frac{x+2}{2014}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\)

\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)

\(\Leftrightarrow\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)

\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)

\(\Leftrightarrow x+2016=0\).Do \(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\ne0\)

\(\Leftrightarrow x=-2016\)

\(\left\{-2016\right\}\)

dap an dung chac la 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 \(x\in\left\{-2016\right\}\)

bạn cộng thêm 1 vào mỗi phân thức đó 

sau đó sẽ có phân tử chung là x+2016

kết quả là x=-2016

thật ra bài này là bài toán lớp 6 

/x+2014/+2015=2016

=>/x+2014/=2016-2015

=>/x+2014/=1

=>x+2014=1 hoặc x+2014=-1

*nếu x+2014=1

=>            x=1-2014

=>            x=-2013

*nếu x+2014=-1

=>             x=-1-2014

=>             x=-2015

vậy x thuộc {-2015;-2013}

mk thi rùi đúng 100%

|x + 2014| + 2015 = 2016

=> |x + 2014| = 2016 - 2015

=> |x + 2014| = 1

+) x + 2014 = 1

=> x = 1 - 2014

=> x = -2013

+) x + 2014 = -1

=> x = -1 - 2014

=> x = -2015

Vậy S = {-2015; -2013}.

Ta có:|x+2014|+2015=2016

=>|x+2014|=1

TH1:x+2014=-1

=>x=-2015

TH2:x+2014=1

=>x=-2013

Vậy x=-2015;-2013

bn đg lm violympic à mình viết đáp án trc nhé tí sẽ có lời giải

S={-3;3}

<=>(|x-2013|+2014)(x²+5)(9-x²)=-(x-3)(x+3)(x²+5)(|x-2013|+2014)

=>-(x-3)(x+3)(x²+5)(|x-2013|+2014=0

=>x=±3 hay x=-3 hoặc3

vậy S={±3}

S=-3;3 mình thề luôn nhớ k^_^

| x + 2014 | + 2015 = 2016

=> | x + 2014 | = 2016 - 2015

=> | x + 2014 | = 1

=> x + 2014 = 1 hoặc - 1

TH1 : x + 2014 = 1 => x = 1 - 2014 => x = - 2013

TH2 : x + 2014 = - 1 => x = - 1 - 2014 => x = - 2015

Vậy x = -2013 hoặc x = - 2015