Question

so sánh

\(\frac{200}{201}\)+\(\frac{201}{202}\)và \(\frac{200+201}{201+202}\)

A=\(\frac{54\cdot107-53}{53\cdot107+54}\)và B=\(\frac{135\cdot269-133}{134\cdot269+135}\)

Answer 1

\(\frac{200}{201}+\frac{201}{202}>\frac{200}{201+202}+\frac{201}{201+202}=\frac{200+201}{201+202}\)

\(A=\frac{54.107-53}{53.107+54}=\frac{\left(53+1\right)107-53}{53.107+54}=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)

\(B=\frac{135.269-133}{134.269+135}=\frac{\left(134+1\right)269-133}{134.269+135}=\frac{134.269+269-133}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)

Vậy A<B

Answer 2

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