Question

Chứng minh rằng nếu  a/b=c/d (Với b,d ¹ 0)  ta suy ra  : a/b=a+2c/b+2d.

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

\(\dfrac{a}{b}=\dfrac{bk}{b}=k\)

\(\dfrac{a+2c}{b+2d}=\dfrac{bk+2dk}{b+2d}=k\)

Do đó: a/b=a+2c/b+2d

Answer 2

cho mình sửa lại tí (vs b,d khác 0)

Answer 3

Đặt \(\dfrac{a}{b}=k;\dfrac{c}{d}=k\Rightarrow a=bk;c=dk\)

\(\dfrac{a}{b}=\dfrac{bk+2dk}{b+2d}=k\)

vậy ta có đpcm 

 

Answer 4

Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\) ⇒ \(ad=bc\) ⇒ \(ab+ad=ab+bc\)

                        ⇒ \(a\left(b+d\right)=b\left(a+c\right)\Rightarrow\) \(\dfrac{a}{b}=\dfrac{a+2c}{b+2d}\)