Ta có:
\(\dfrac{a}{b}=\dfrac{c}{d}\)
\(\Rightarrow\dfrac{c}{a}=\dfrac{d}{b}\)
\(\dfrac{2a+c}{a}=\dfrac{2a}{a}+\dfrac{c}{a}=2+\dfrac{c}{a}\)
\(\dfrac{2b+d}{b}=\dfrac{2b}{b}+\dfrac{d}{b}=2+\dfrac{d}{b}=2+\dfrac{c}{a}\left(\text{Vì }\dfrac{d}{b}=\dfrac{c}{a}\right)\)
\(\Rightarrow\dfrac{2a+c}{a}=\dfrac{2b+d}{b}\)
\(\Rightarrow\dfrac{a}{2a+c}=\dfrac{b}{2b+d}\)
\(\RightarrowĐPCM\)
Ta có:
\(\dfrac{a}{b}=\dfrac{c}{d}\)
\(\Rightarrow\dfrac{c}{a}=\dfrac{d}{b}\)
\(\dfrac{2a+c}{a}=\dfrac{2a}{a}+\dfrac{c}{a}=2+\dfrac{c}{a}\)
\(\dfrac{2b+d}{b}=\dfrac{2b}{b}+\dfrac{d}{b}=2+\dfrac{d}{b}=2+\dfrac{c}{a}\left(\text{Vì }\dfrac{d}{b}=\dfrac{c}{a}\right)\)
\(\Rightarrow\dfrac{2a+c}{a}=\dfrac{2b+d}{b}\)
\(\Rightarrow\dfrac{a}{2a+c}=\dfrac{b}{2b+d}\)
\(\RightarrowĐPCM\)
