Question

Cho tỉ lệ thức a/b=c/d chứng minh rằng

a,a+b/b=c+d/d     b,a/a+b=c/c+d      c,a-b/b=c-d/d     d, a/a-b=c/c-d

   Các bạn giúp mình nhé, cảm ơn nhiều

Answer 1

Ta có \(\frac{a}{b}=\frac{c}{d}\)

a) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{b}+1=\frac{c}{d}+1\Rightarrow\frac{a+b}{b}=\frac{c+d}{d}\)

b) \(\frac{a}{c}=\frac{a+b}{c+d}\Rightarrow\frac{a}{a+b}=\frac{c}{c+d}\)

c) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{b}-1=\frac{c}{d}-1\Rightarrow\frac{a-b}{b}=\frac{c-d}{d}\)

d) \(\frac{a}{b}=\frac{c}{d}\Rightarrow1:\frac{a}{b}=1:\frac{c}{d}\Rightarrow\frac{b}{a}=\frac{d}{c}\Rightarrow1-\frac{b}{a}=1-\frac{d}{c}\Rightarrow\frac{a-b}{a}=\frac{c-d}{c}\Rightarrow1:\frac{a-b}{a}=1:\frac{c-d}{c}\)

\(\Rightarrow\frac{a}{a-b}=\frac{c}{c-d}\)

Answer 2

Đặt `a/b=c/d =k ->a=bk, c=dk`

`a,`

`(a+b)/b=(bk +b)/b=(b (k+1) )/b=k+1`

`(c+d)/d=(dk +d)/d=(d (k+1) )/d=k+1`

`-> (a+b)/b=(c+d)/d`

`b,`

`a/(a+b)=(bk)/(bk+b)=(bk)/(b(k+1) )=k/(k+1)`

`c/(c+d)=(dk)/(dk+d)=(dk)/(d(k+1) ) = k/(k+1)`

`-> a/(a+b)=c/(c+d)`

`c,`

`(a-b)/b=(bk-b)/b=(b(k-1) )/b=k-1`

`(c-d)/d=(dk-d)/d=(d(k-1) )/d=k-1`

`-> (a-b)/b=(c-d)/d`

`d,`

`a/(a-b) =(bk)/(bk-b)=(bk)/(b(k-1) )=k/(k-1)`

`c/(c-d)=(dk)/(dk-d)=(dk)/(d(k-1) )=k/(k-1)`

`-> a/(a-b)=c/(c-d)`