\(\frac{3a-b}{a+b}=\frac{3}{4}\Leftrightarrow12a-4b=3a+3b\Leftrightarrow9a=7b\Leftrightarrow\frac{a}{b}=\frac{7}{9}\)

a/

3a−ba+b =3(a+b)−4ba+b =3−4ba+b =34 .

⇒4ba+b =94 ⇒9a+9b=16b⇒9a=7b⇒ab =79 

\(\frac{3a-b}{a+b}=\frac{3}{4}\)

\(\Leftrightarrow4\left(3a-b\right)=3\left(a+b\right)\)

\(\Leftrightarrow12a-4b=3a+3b\)

\(\Leftrightarrow12a-3a=3b+4b\)

\(\Leftrightarrow9a=7b\)

\(\Leftrightarrow\frac{a}{b}=\frac{7}{9}\)

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

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

\(\frac{a}{10}=\frac{b}{11}=\frac{c}{12}\)

\(\frac{a}{10}=\frac{b}{11}=\frac{c}{12}\)

\(\Leftrightarrow\)\(\frac{a}{10}=\frac{6b}{66}=\frac{8c}{96}=\frac{a+6b-8c}{10+66-96}\)(*)

và: \(\frac{a}{10}=\frac{3b}{33}=\frac{4c}{48}=\frac{a+3b-4c}{10+33-48}\) (**)

lấy (*) chia (**) được kết quả P=\(\frac{1}{4}\)

a;b;c tỉ lệ với 10;11;12 => \(\frac{a}{10}=\frac{b}{11}=\frac{c}{12}\)

Đặt \(\frac{a}{10}=\frac{b}{11}=\frac{c}{12}=k\Rightarrow a=10k;b=11k;c=12k\) Thay vào P ta được :

\(P=\frac{10k+6.11k-8.12k}{10k+3.11k-4.12k}=\frac{k\left(10+6.11-8.12\right)}{k\left(10+3.11-4.12\right)}=\frac{10+66-96}{10+33-56}=\frac{-20}{-13}=\frac{20}{13}\)