Toán Lớp 7: Chứng minh rằng nếu
$\frac{a}{b}$= $\frac{c}{d}$$\neq$ 1 thì $\frac{a+b}{a-b}$= $\frac{c+d}{c-d}$ với a,b,c$\neq$0
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Toán Lớp 7: Chứng minh rằng nếu
$\frac{a}{b}$= $\frac{c}{d}$$\neq$ 1 thì $\frac{a+b}{a-b}$= $\frac{c+d}{c-d}$ với a,b,c$\neq$0
Comments ( 2 )
Đặt $\frac{a}{b}$=$\frac{c}{d}$=k
⇒a=bk
⇒c=dk
⇒$\frac{a+b}{a-b}$=$\frac{bk+b}{bk-b}$=$\frac{b(k+1)}{b(k-1)}$=$\frac{k+1}{k-1}$(1)
⇒$\frac{c+d}{c-d}$=$\frac{dk+d}{dk-d}$=$\frac{d(k+1)}{d(k-1)}$=$\frac{k+1}{k-1}$(2)
Từ(1)và(2)⇒$\frac{a+b}{a-b}$=$\frac{c+d}{c-d}$(đpcm)