Question

chứng minh rằng nếu a/b = c/d khác 1 ( a; b; c; d; khác 0; akhác b; c khác d ) thì :

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

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

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

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

Answer 1

a: Đặt a/b=c/d=k

=>a=bk; c=dk

\(\dfrac{a+b}{a}=\dfrac{bk+b}{bk}=\dfrac{k+1}{k}\)

\(\dfrac{c+d}{c}=\dfrac{dk+d}{dk}=\dfrac{k+1}{k}\)

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

b: \(\dfrac{a-b}{a}=\dfrac{bk-b}{bk}=\dfrac{k-1}{k}\)

\(\dfrac{c-d}{c}=\dfrac{dk-d}{dk}=\dfrac{k-1}{k}\)

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

c: \(\dfrac{a}{a+b}=\dfrac{bk}{bk+b}=\dfrac{k}{k+1}\)

\(\dfrac{c}{c+d}=\dfrac{dk}{dk+d}=\dfrac{k}{k+1}\)

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