Tu ti le thuc: a/b = c/d => d/c = b/a

Ta co: 

(a+b)/a = (c+d)/c

=> 1  + b/a = 1 + d/c 

Do d/c = b/a   (cmt) nen suy ra:

(a+b)/a = (c+d)/c

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

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

\(\Rightarrow\)1-\(\frac{a}{b}\)= 1- \(\frac{c}{d}\)

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

thanks bạn

đừng nói đây là bài tập về nhà của bạn đấy!!!!!!!!!!!

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{a^2-b^2}{c^2-d^2}\)mà\(\frac{a^2}{c^2}=\frac{a}{c}.\frac{a}{c}=\frac{a}{c}.\frac{b}{d}=\frac{ab}{cd}\Rightarrow\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}\)

a/b=c/d

=>ad=bc

=>ac-ad=ac-bc

=>a(c-d)=c(a-b)

=>(a-b)/a=(c-d)/c

a/b=c/d=>ad=bc

=>b/a=d/c

=>1-b/a=1-d/c

=>a-b/a=c-d/c

=>đpcm

\(\text{Vì }\frac{a}{b}=\frac{c}{d}\text{ nên :}\frac{a}{c}=\frac{b}{d}\)

\(\text{Mặt khác: }\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\)

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

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

\(\dfrac{a}{b}=\dfrac{c}{d}\)

=>\(\dfrac{a}{b}-1=\dfrac{c}{d}-1\)

=>\(\dfrac{a-b}{b}=\dfrac{c-d}{d}\)

a/b=c/b => a/c=b/d, d/b=c/a, d/c=b/a