\(\frac{\left|x\right|+2015}{2016}\) . Có: \(\left|x\right|\ge0\Rightarrow\left|x\right|+2015\ge2015\Rightarrow\frac{\left|x\right|+2015}{2016}\ge\frac{2015}{2016}\)

Dấu = xảy ra khi \(x+2015=0\Rightarrow x=0\)

Vậy \(Min\frac{\left|x\right|+2015}{2016}=\frac{2015}{2016}\) tại \(x=0\)

\(\frac{\left|x\right|+1996}{-1997}\) có \(\left|x\right|\ge0\Rightarrow\left|x\right|+1996\ge1996\Rightarrow\frac{\left|x\right|+1996}{-1997}\le-\frac{1996}{1997}\)

Dấu = xảy ra khi \(\left|x\right|+1996=1996\Rightarrow x=0\) 

Vậy \(Max\frac{\left|x\right|+1996}{-1997}=\frac{1996}{-1997}\) tại \(x=0\)

\(\frac{1996}{\left|x\right|+1997}\) có \(\left|x\right|+1997\ge0\Rightarrow\left|x\right|+1997\ge1997\Rightarrow\frac{1996}{\left|x\right|+1997}\le\frac{1996}{1997}\)

Dấu = xảy ra khi \(x+1997=1997\Rightarrow x=0\)

Vậy \(Max\frac{1996}{\left|x\right|+1997}=\frac{1996}{1997}\) tại \(x=0\)

1.\(\frac{1996}{\left|x\right|+1997}\)có GTLN \(\Leftrightarrow\left|x\right|+1997\)có GTNN.

Mà \(\left|x\right|+1997\ne0\)

Ta thấy: \(\left|x\right|\ge0\forall x\in R\Rightarrow\left|x\right|+1997\ge1997\)

\(\Rightarrow\left|x\right|=0\)thì \(\left|x\right|+1997\)có GTNN  là \(1997\)

\(\Rightarrow\)GTLN của \(\frac{1996}{\left|x\right|+1997}\)là \(\frac{1996}{1997}\)khi x=0

 2.\(\frac{\left|x\right|+1996}{-1997}=\frac{-\left(\left|x\right|+1996\right)}{1997}\)

\(\Rightarrow\left|x\right|+1996\)phải có GTNN thì \(\frac{\left|x\right|+1996}{-1997}\)đạt GTLN

Mà \(\left|x\right|\ge0\forall x\in R\Rightarrow x=0\)thì \(\left|x\right|+1996\)có GTNN là \(1996\)

Vậy GTLN của \(\frac{\left|x\right|+1996}{-1997}\)là \(\frac{1996}{-1997}\)khi x=0

mình cùng có tên là Minh Thư đó

ta có |x|≥0  => |x| +1996 ≥ 1996  

=> |x| +1996/-1997   ≤ 1996/-1997

=> A  ≤1996/-1997

=> GTLN A = 1996/-1997

dấu "=" xảy ra <=> x=0

vậy GTLN A =1996/-1997 <=> x=0

a/Viết đề mà cx sai đc nữa: \(\left(\frac{x+2}{98}+1\right)\left(\frac{x+3}{97}+1\right)=\left(\frac{x+4}{96}+1\right)\left(\frac{x+5}{95}+1\right)\)

\(\Leftrightarrow\frac{x+100}{98}.\frac{x+100}{97}-\frac{x+100}{96}.\frac{x+100}{95}=0\)

\(\Leftrightarrow\left(x+100\right)^2\left(\frac{1}{98.97}-\frac{1}{96.95}\right)=0\)

\(\Rightarrow x=-100\)

b/\(\Leftrightarrow\left(\frac{x+1}{1998}+1\right)+\left(\frac{x+2}{1997}+1\right)=\left(\frac{x+3}{1996}+1\right)+\left(\frac{x+4}{1995}+1\right)\)

\(\Leftrightarrow\frac{x+1999}{1998}+\frac{x+1999}{1997}-\frac{x+1999}{1996}-\frac{x+1999}{1995}=0\)

\(\Leftrightarrow\left(x+1999\right)\left(...\right)=0\Rightarrow x=-1999\)

b,\(\frac{x+1}{1998}+\frac{x+2}{1997}=\frac{x+3}{1996}+\frac{x+4}{1995}\)

=>\(\frac{x+1}{1998}+1\frac{x+2}{1997}+1=\frac{x+3}{1996}+1+\frac{x+4}{1995}+1\)

\(\Leftrightarrow\)\(\frac{x+1999}{1998}+\frac{x+1999}{1997}=\frac{x+1999}{1996}+\frac{x+1999}{1995}\)

\(\Leftrightarrow\)\(\frac{x+1999}{1998}+\frac{x+1999}{1997}-\frac{x+1999}{1996}-\frac{x+1999}{1995}\)=0

\(\Leftrightarrow\)\(\left(x+1999\right)\left(\frac{1}{1998}+\frac{1}{1997}-\frac{1}{1996}-\frac{1}{1995}\right)\)=0

\(\Leftrightarrow\)x+1999=0(Vì \(\frac{1}{1998}+\frac{1}{1997}-\frac{1}{1996}-\frac{1}{1995}\ne0\))

\(\Leftrightarrow\)x=-1999

Vậy x=-1999

GTLN là -1