Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) .Cmr:

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

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

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

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

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

Do đó: \(\dfrac{a+c}{b+d}=\dfrac{a-c}{b-d}\)

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

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

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