Câu hỏi của Đinh Xuân An

Question

CMR: a/b=c/d thì a/b = (a cộng hoặc trừ c) / (b cộng hoặc trừ d)

Nguyễn thành Đạt · Accepted Answer

Ta có : $\dfrac{a}{b}=\dfrac{c}{d}\text{=}t$

$\dfrac{a-c}{b-d}\text{=}\dfrac{bt-dt}{b-d}\text{=}\dfrac{t\left(b-d\right)}{b-d}\text{=}t$

$\dfrac{a+c}{b+d}\text{=}\dfrac{bt+dt}{b+d}\text{=}\dfrac{t\left(b+d\right)}{b+d}\text{=}t$

$\Rightarrow\dfrac{a}{b}\text{=}\dfrac{a-c}{b-d}\text{=}\dfrac{a+c}{b+d}$Câu trả lời: Ta có : $\dfrac{a}{b}=\dfrac{c}{d}\text{=}t$

$\dfrac{a-c}{b-d}\text{=}\dfrac{bt-dt}{b-d}\text{=}\dfrac{t\left(b-d\right)}{b-d}\text{=}t$

$\dfrac{a+c}{b+d}\text{=}\dfrac{bt+dt}{b+d}\text{=}\dfrac{t\left(b+d\right)}{b+d}\text{=}t$

$\Rightarrow\dfrac{a}{b}\text{=}\dfrac{a-c}{b-d}\text{=}\dfrac{a+c}{b+d}$