Question

Chứng minh rằng :

Nếu \(\dfrac{a}{b}=\dfrac{c}{d}\) thì \(\dfrac{a+b}{b}=\dfrac{c+d}{d}\) (với a,b,c,d \(\ne\) 0)

Answer 1

ta có : \(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow1+\dfrac{a}{b}=1+\dfrac{c}{d}\Leftrightarrow\dfrac{a+b}{b}=\dfrac{c+d}{d}\left(đpcm\right)\)

Answer 2

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=>\(a=b\cdot k\) ;\(c=d\cdot k\)

=>\(\dfrac{a+b}{b}=\dfrac{b\cdot k+b}{b}=\dfrac{b\cdot\left(k+1\right)}{b}=k+1\) (1)

=>\(\dfrac{c+d}{d}=\dfrac{d\cdot k+d}{d}=\dfrac{d\cdot\left(k+1\right)}{d}=k+1\) (2)

Từ (1) và (2) => \(\dfrac{a+b}{b}=\dfrac{c+d}{d}\)