Question

Giải hộ Mỹ bài 3 ạ. Chắc phải học lại lớp 7 thôi(٥↼_↼)

Answer 1

a) \(\dfrac{a}{b}-\dfrac{a+c}{b+c}=\dfrac{a\left(b+c\right)-b\left(a+c\right)}{b\left(b+c\right)}=\dfrac{ab+ac-ab-bc}{b\left(b+c\right)}=\dfrac{ac-bc}{b\left(b+c\right)}=\dfrac{c\left(a-b\right)}{b\left(b+c\right)}< 0\)

Do \(a< b\Leftrightarrow a-b< 0\) và \(b>0,c>0\))

\(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+c}\)

b) \(\dfrac{a}{b}-\dfrac{a+c}{b+c}=\dfrac{a\left(b+c\right)-b\left(a+c\right)}{b\left(b+c\right)}=\dfrac{ab+ac-ab-bc}{b\left(b+c\right)}=\dfrac{ac-bc}{b\left(b+c\right)}=\dfrac{c\left(a-b\right)}{b\left(b+c\right)}>0\)

(do \(a>b\Leftrightarrow a-b>0\) và \(b>0,c>0\))

\(\Rightarrow\dfrac{a}{b}>\dfrac{a+c}{b+c}\)