Question

cho tỉ lệ thức 

\(\frac{a-3}{a+3}\)=\(\frac{b-6}{b+6}\) với a khác -3, b khác -6 cmr \(\frac{a}{b}\)=\(\frac{1}{2}\)

         Cần Gấp 

Answer 1

\(\frac{a-3}{a+3}=\frac{b-6}{b+6}\Rightarrow\left(a-3\right).\left(b+6\right)=\left(b-6\right).\left(a+3\right)\)

\(\Rightarrow ab+6a-3b-18=ab+3b-6a=18\)

\(\Rightarrow b.\left(a-3\right)+6.a-18=a.\left(b-6\right)+3.b-18\)

\(\Rightarrow b.\left(a-3\right)+6a=a.\left(b-6\right)+3b\)

\(\Rightarrow ab-3b=ab-6a+3b-6a\)

\(\Rightarrow ab-3b=ab-3.\left(4a-b\right)\)

\(b=4a-b\Rightarrow2b=4a\Rightarrow b=2a\Rightarrow\frac{a}{b}=\frac{1}{2}\)