Question

Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh rằng

a) \(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a+4c}{b+4d}\)

b) \(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{3a+2c}{3b+2d}\)

c) \(\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-2b}{c-2d}\)

d) \(\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{5a-2b}{5c-2d}\)

Answer 1

a) ta có : \(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow\dfrac{a}{b}=\dfrac{4c}{4d}=\dfrac{a+4c}{b+4d}\left(đpcm\right)\)

b;c;d tương tự hết

Answer 2

b: a/b=c/d

nên 3a/3b=2c/2d

=>a/b=c/d=(3a+2c)/(3b+2d)

c: a/c=b/d nên a/c=2b/2d=(a-2b)/(c-2d)

d: a/c=b/d

nên 5a/5c=2b/2d

=>a/c=b/d=(5a-2b)/(5c-2d)