Toán Lớp 6: text(Bài 4: Cho) $\frac{a}{b}$ = $\frac{c}{d}$ . Chứng tỏ rằng: $\frac{a}{b}$ = $\frac{a + c}{b + d}$
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Toán Lớp 6: text(Bài 4: Cho) $\frac{a}{b}$ = $\frac{c}{d}$ . Chứng tỏ rằng: $\frac{a}{b}$ = $\frac{a + c}{b + d}$
Chi tiết nha ????
Comments ( 2 )
Đặt a/b = c/d = k
=> a =bk; c = dk
Có:
(a + c)/(b + d) = (bk + dk)/(b + d) = ((b + d)k)/(b + d) = k
Mà a/b = k
=> a/b = (a + c)/(b + d)
Đặt a/b=c/d=a/c=b/d=k=>a=ck;b=dk
Ta có:
a/b=ck/dk=c/d(1)
(a+c)/(b+d)=(ck+c)/(dk+d)=(c(k+1))/(d(k+1))=c/d(2)
Từ (1);(2)=>a/b=(a+c)/(b+d)(đpcm)