Question

Cho \(\frac{a}{b}=\frac{c}{d}\). CMR \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)

Answer 1

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

\(\Rightarrow\frac{a+b}{a-b}=\frac{bk+b}{bk-b}=\frac{b\left(k+1\right)}{b\left(k-1\right)}=\frac{k+1}{k-1}\)

\(\frac{c+d}{c-d}=\frac{dk+d}{dk-d}=\frac{d\left(k+1\right)}{d\left(k-1\right)}=\frac{k+1}{k-1}\)

\(\RightarrowĐPCM\)

Answer 2

Ta có :\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

Ap dung tinh chat cua day ti so bang nhau:

\(\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a+b}{c+d}=\frac{a-b}{c-b}\)

\(\Rightarrow\frac{a+b}{c+d}=\frac{a-b}{c-d}\Rightarrow\frac{a+b}{a-d}=\frac{c+d}{c-d}\)

Answer 3

Từ \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

Áp dụng t/c dãy tỉ số bằng nhau  :\(\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}=\frac{a-b}{c-d}\)

Từ \(\frac{a+b}{c+d}=\frac{a-b}{c-d}\Rightarrow\frac{a+b}{a-b}=\frac{c+d}{c-d}\left(ĐPCM\right)\)

Answer 4

Ta có; \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

Theo t/c dãy ts = nhau

\(\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}=\frac{a-b}{c-d}\)

\(\RightarrowĐpcm\)

Answer 5

đáp số 

\(\frac{c+d}{c-d}\)

hok tốt

Answer 6

đáp số 

c + d / c - d

hok tốt