Question

Cho:(a+3).(b-4)-(a-3).(b+4)=0
CMR : a/3=b/4

 

Answer 1

\(\left(a+3\right).\left(b-4\right)-\left(a-3\right).\left(b+4\right)=0\)

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

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

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

\(\frac{a}{a+3}=\frac{b}{b+4}\Rightarrow a.\left(b+4\right)=b.\left(a+3\right)\Rightarrow ab+4a=ab+3b\)

\(\Rightarrow4a=3b\Rightarrow\frac{a}{3}=\frac{b}{4}\left(đpcm\right)\)