Question

Cho a,b,c,d khác 0; \(\dfrac{a}{b}\) = \(\dfrac{c}{d}\)

Chứng tỏ rằng \(\dfrac{2a-5}{3a}\)=\(\dfrac{2c-5d}{3c}\)

Các bạn giúp mình với mình đang cần gấp.Thanks!!!

Answer 1

Đề sai :(

Sửa:

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) \(\left(a;b;c;d\ne0\right).\)

Chứng tỏ rằng: \(\dfrac{2a-5b}{3a}=\dfrac{2c-5d}{3c}.\)

Giải:

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

Ta có:

\(\dfrac{2a-5b}{3a}=\dfrac{2bk-5b}{3bk}=\dfrac{2.5.b\left(k-1\right)}{3bk}=\dfrac{10\left(k-1\right)}{3k}_{\left(1\right)}.\)

\(\dfrac{2c-5d}{3c}=\dfrac{2dk-5d}{3dk}=\dfrac{2.5.d\left(k-1\right)}{3dk}=\dfrac{10\left(k-1\right)}{3k}_{\left(2\right)}.\)

Từ \(_{\left(1\right)\&\left(2\right)}\Rightarrow\dfrac{2a-5b}{3a}=\dfrac{2c-5d}{3c}.\)

\(\Rightarrowđpcm.\)

Answer 2

chỗ kia mình viết sai nha đề đúng là\(\dfrac{2a-5b}{3a}\)=\(\dfrac{2c-5d}{3c}\)