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\(\frac{3a-b}{a+b}=\frac{3}{4}\Leftrightarrow12a-4b=3a+3b\Leftrightarrow9a=7b\Leftrightarrow\frac{a}{b}=\frac{7}{9}\)
\(\frac{3a-b}{a+b}=\frac{3}{4}\)
\(\Leftrightarrow4\left(3a-b\right)=3\left(a+b\right)\)
\(\Leftrightarrow12a-4b=3a+3b\)
\(\Leftrightarrow12a-3a=3b+4b\)
\(\Leftrightarrow9a=7b\)
\(\Leftrightarrow\frac{a}{b}=\frac{7}{9}\)
a/
\(\frac{3a-b}{a+b}=\frac{3\left(a+b\right)-4b}{a+b}=3-\frac{4b}{a+b}=\frac{3}{4}.\)
\(\Rightarrow\frac{4b}{a+b}=\frac{9}{4}\Rightarrow9a+9b=16b\Rightarrow9a=7b\Rightarrow\frac{a}{b}=\frac{7}{9}\)
b/
\(\frac{a}{b}=\frac{3}{7}\Rightarrow\frac{a}{3}=\frac{b}{7}=\frac{3a}{9}=\frac{4b}{28}=\frac{3a-4b}{9-28}=\frac{3a-4b}{-19}\)
\(\frac{a}{3}=\frac{b}{7}\Rightarrow\frac{2a}{6}=\frac{3b}{21}\Rightarrow\frac{2a+3b}{6+21}=\frac{2a+3b}{27}\)
\(\Rightarrow\frac{3a-4b}{-19}=\frac{2a+3b}{27}\Rightarrow\frac{3a-4b}{2a+3b}=-\frac{19}{27}\)
=>(3a-b).4=3.(a+b)
=>12a-4b=3a+3b
=>12a-3a=4b+3b
=>9a=7b
=>a/b=7/9
Tĩk nhé
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\frac{a}{c}=\frac{a-b}{c-d}\Rightarrow\frac{c-d}{c}=\frac{a-b}{a}\)
\(\frac{a}{10}=\frac{b}{11}=\frac{c}{12}\)
\(\Leftrightarrow\)\(\frac{a}{10}=\frac{6b}{66}=\frac{8c}{96}=\frac{a+6b-8c}{10+66-96}\)(*)
và: \(\frac{a}{10}=\frac{3b}{33}=\frac{4c}{48}=\frac{a+3b-4c}{10+33-48}\) (**)
lấy (*) chia (**) được kết quả P=\(\frac{1}{4}\)