Question

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

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

Answer 1

a.Vì \(\dfrac{a}{b}=\dfrac{c}{d}\)

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

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

b.Vì\(\dfrac{a}{b}=\dfrac{c}{d}\)

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

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

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

Answer 2

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

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

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

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

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