\(\frac{a+b}{b+b}=\frac{a}{2.b}+\frac{b}{2.b}=\frac{a}{b}.\frac{1}{2}+\frac{1}{2}\)
\(\Rightarrow\frac{a}{b}.\frac{1}{2}+\frac{1}{2}=\frac{a}{b}.4\Rightarrow\frac{1}{2}=\frac{a}{b}.4-\frac{a}{b}.\frac{1}{2}\Rightarrow\frac{1}{2}=a.\frac{7}{2}\)
\(\Rightarrow\frac{a}{b}=\frac{1}{2}:\frac{7}{2}\Rightarrow\frac{a}{b}=\frac{1}{7}\)