Question

So sánh:

A=\(\frac{n+1}{-n-2}\) và B=\(\frac{-n-2}{n+3}\)

Answer 1

Ta có :   \(\left(-n-2\right).\left(-n-2\right)\)

\(=\left(-n-2\right).-n-\left(-n-2\right).2\)

\(=\left(-n\right).\left(-n\right)-2.\left(-n\right)-\left[-n.2-2.2\right]\)

\(=n^2+2n+2n+4\)

\(=n^2+4n+4\)( 1 ) 

\(\left(n+1\right)\left(n+3\right)\)

\(=\left(n+1\right).n+\left(n+1\right).3\)

\(=n^2+n+3n+3\)( 2 ) 

Từ ( 1 ) ; ( 2 ) 

\(\Rightarrow\left(-n-2\right)\left(-n-2\right)>\left(n+1\right)\left(n+3\right)\)

\(\Rightarrow\frac{n+1}{-n-2}>\frac{-n-2}{n+3}\)

Chúc bạn học tốt !!!!