(-1999) - (-234-1999)
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a ) ( 1456 + 323 ) - 1456
= 1456 + 323 - 1456
= ( 1456 - 1456 ) + 323 = 323
b ) ( - 1999 ) - ( - 234 - 1999)
= - 1999 + 234 + 1999
= ( - 1999 + 1999 ) + 234 = 0 + 234 = 234
![](https://rs.olm.vn/images/avt/0.png?1311)
a.(1456+23)-1456
=1456+23-1456
=(1456-1456)+23
=23
b.(-1999)-(-234-1999)
=-1999-(-234)+1999
=(-1999+1999)-(-234)
=-(-234)
=234
c.(116+124)+(215-116-124)
=116+124+215-116-124
=(166-166)+(124-124)+215
=215
d.(435-167-89)-(435-89)
=435-167-89-435+89
=(435-435)-(89-89)-167
=-167
k for more
#hungB
a) = 1456 + 23 - 1456
= ( 1456 - 1456 ) + 23
= 0 + 23
= 23
b) = ( -1999 ) + 234 + 1999
= ( -1999 + 1999 ) + 234
= 0 + 234
= 234
c) = 116 + 124 + 215 - 116 - 124
= ( 116 - 116 ) + ( 124 - 124 ) + 215
= 0 + 0 + 215
= 215
d) = 435 - 167 - 89 - 435 + 89
= ( 435 - 435 ) + ( -89 + 89 ) - 167
= 0 + 0 - 167
= -167
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 3/4 < 1
115/14 > 1
=> 3/4 < 115/14
b) 2000/1999 > 1
1998/1999 < 1
=> 2000/1999>1998/1999
c)-17/234 < 0 , 1/1995 > 0
=> -17/234 < 1/1995
d) 23/-15 < 0 ; -17/-49>0
=> 23/-15 < -17/-49
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}\)
\(\dfrac{1}{1999}A=\dfrac{1999^{1999}+1}{1999^{1999}+1999}\)
\(\dfrac{1}{1999}A=\dfrac{1999^{1999}}{1999^{1999}}-\dfrac{1998}{1999^{1999}+1999}\)
\(\dfrac{1}{1999}A=1-\dfrac{1998}{1999^{1999}+1999}\)
\(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}\)
\(\dfrac{1}{1999}B=\dfrac{1999^{2000}+1}{1999^{2000}+1999}\)
\(\dfrac{1}{1999}B=\dfrac{1999^{2000}}{1999^{2000}}-\dfrac{1998}{1999^{2000}+1999}\)
\(\dfrac{1}{1999}B=1-\dfrac{1998}{1999^{2000}+1999}\)
Vì \(\dfrac{1998}{1999^{1999}+1999}>\dfrac{1998}{1999^{2000}+1999}=>\dfrac{1}{1999}A< \dfrac{1}{1999}B=>A< B\)
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}=\dfrac{\left(1999^{1999}+1\right)^2}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(A=\dfrac{\left(1999^{1999}\right)^2+2.1999^{1999}+1}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\left(1\right)\)
\(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}=\dfrac{\left(1999^{2000}+1\right)\left(1999^{1998}+1\right)}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(B=\dfrac{\left(1999.1999^{1999}+1\right)\left(\dfrac{1}{1999}.1999^{1999}+1\right)}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(B=\dfrac{\left(1999^{1999}\right)^2+1999.1999^{1999}+\dfrac{1}{1999}.1999^{1999}+1}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(B=\dfrac{\left(1999^{1999}\right)^2+\left(1999+\dfrac{1}{1999}\right).1999^{1999}+1}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\left(2\right)\)
mà \(\left(1999+\dfrac{1}{1999}\right)>2\)
\(\left(1\right).\left(2\right)\Rightarrow A< B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
So sánh
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}\) ; \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}\)
Ta có: \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}>1\) ( vì tử > mẫu )
Do đó: \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}>\dfrac{1999^{2000}+1+1998}{1999^{1999}+1+1998}=\dfrac{1999^{2000}+1999}{1999^{1999}+1999}=\dfrac{1999.\left(1999^{1999}+1\right)}{1999.\left(1999^{1998}+1\right)}=\dfrac{1999^{1999}+1}{1999^{1998}+1}=A\)
Vậy B > A
Chúc bạn học tốt
(-1999) - (-234-1999)
=(-1999) -(-2233)
=-4232