Question

từ TLT \(\frac{a}{b}=\frac{c}{d}\) , hãy suy ra TLT sau:

\(\frac{a}{a+b}=\frac{c}{c+d}\) (a+b khác 0, c+d khác 0)

Answer 1

Ta có: \(\frac{a}{b}=\frac{c}{d}.\)

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

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

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

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

\(\Rightarrow\frac{a}{a+b}=\frac{c}{c+d}\left(đpcm\right).\)

Chúc bạn học tốt!

Answer 2

Đặt \(\frac{a}{b}=\frac{c}{d}=k\) (k\(\in\)N*)

\(\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

Thay vào ta có:

\(\frac{a}{a+b}=\frac{bk}{bk+b}=\frac{bk}{b\left(k+1\right)}=\frac{k}{k+1}\)

\(\frac{c}{c+d}=\frac{dk}{dk+d}=\frac{dk}{d\left(k+1\right)}=\frac{k}{k+1}\)

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

Vậy \(\frac{a}{a+b}=\frac{c}{c+d}\)(điều phải chứng minh)

Hok tốt nha!!!