Nguyễn Huy Tú chắc làm sai rồi
Chứng minh:
Ta có: \(\dfrac{2a+13b}{3a-7b}=\dfrac{2c+13d}{3c-7d}\)
\(\Rightarrow\dfrac{2a+13b}{2c+13d}=\dfrac{3a-7b}{3c-7d}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{2a+13b}{2c+13d}=\dfrac{3a-7b}{3c-7d}=\dfrac{2a+13b+3a-7b}{2c+13d+3c-7d}=\dfrac{5a+6b}{5c+6d}\)
\(\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\Rightarrow\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\left\{{}\begin{matrix}a=b\\c=d\end{matrix}\right.\Rightarrow\dfrac{a}{a}=\dfrac{c}{c}\)
\(\Rightarrow\dfrac{a+a}{a}=\dfrac{c+c}{c}\Rightarrow\dfrac{a+b}{b}=\dfrac{c+d}{d}\)
Vậy \(\dfrac{a+b}{b}=\dfrac{c+d}{d}\) (Đpcm)
Giải:
Ta có: \(\dfrac{2a+13b}{3a-7b}=\dfrac{2c+13d}{3c-7d}\Rightarrow\dfrac{2a+13b}{2c+13d}=\dfrac{3a-7b}{3c-7d}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{2a+13b}{2c+13d}=\dfrac{3a-7b}{3c-7d}=\dfrac{2a}{2c}=\dfrac{13b}{13d}=\dfrac{3a}{3c}=\dfrac{7b}{7d}=\dfrac{a}{c}=\dfrac{b}{d}\)
\(=\dfrac{a+b}{c+d}\)
Ta thấy \(\dfrac{a+b}{c+d}=\dfrac{b}{d}\Rightarrow\dfrac{a+b}{b}=\dfrac{c+d}{d}\left(đpcm\right)\)
Vậy \(\dfrac{a+b}{b}=\dfrac{c+d}{d}\)
