So sánh \(\frac{54\cdot107-5}{53\cdot107+54}\)và \(\frac{135\cdot269-133}{134\cdot269+135}\)
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\(\frac{200}{201}+\frac{201}{202}>\frac{200}{201+202}+\frac{201}{201+202}=\frac{200+201}{201+202}\)
\(A=\frac{54.107-53}{53.107+54}=\frac{\left(53+1\right)107-53}{53.107+54}=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)
\(B=\frac{135.269-133}{134.269+135}=\frac{\left(134+1\right)269-133}{134.269+135}=\frac{134.269+269-133}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)
Vậy A<B
câu a là
200/201+201/202>200/202+201/202>1
200+201/201+201<1
=>200/201+201/202>1>200+201/201+202
a) Xét \(\frac{1999.2000-2}{1998.1999+3997}=\frac{1999.\left(1998+2\right)-2}{1998.1999+3997}=\frac{1999.1998+1999.2-2}{1998.1999+3997}=\frac{1999.1998+3996}{1998.1998+3997}\)
=> A < B
\(\frac{54.107-53}{53.107-54}=\frac{\left(53+1\right).107-53}{53.107-54}=\frac{53.107+107-53}{53.107-54}=\frac{53.107+54}{53.107-54}=1-1=0\)
THAM KHẢO :
A = 53.107 + 54 53 + 1 .107 − 53
= 53.107 + 54 53.107 + 107 − 53
= 53.107 + 54 53.107 + 54 = 1.
B = 134.269 + 135 134 + 1 .269 − 133
= 134.269 + 135 134.269 + 269 − 133
= 134.269 + 135 134.269 + 136 > 1
⇒A < B
\(\frac{54\times107-53}{53\times107+54}=\frac{53\times107+107-53}{53\times107+54}=\frac{53\times107+54}{53\times107+54}=1\)
\(\frac{135\times269-134}{134\times269+135}=\frac{134\times269+269-134}{134\times269+135}=\frac{134\times269+135}{134\times269+135}=1\)
\(A=\frac{\left(53+1\right).107-53}{53.107+54}=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1.\)
\(B=\frac{\left(134+1\right).269-133}{134.269+135}=\frac{134.269+269-133}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)
\(\Rightarrow A< B\)