Question

Cho ab/a+b=bc/b+c.Chứng minh a/b=b/c

Answer 1

ab/a+b=bc/b+c

=>ab(b+c)=(a+b)bc

=>ab²+abc=abc+b²c

=>ab²=b²c

=>ab=bc

=>a/b=b/c

Answer 2

\(\frac{ab}{a+b}=\frac{bc}{b+c}\Rightarrow\frac{ab}{bc}=\frac{a+b}{b+c}=\frac{a}{c}\)

\(\Rightarrow ab.\left(b+c\right)=bc.\left(a+b\right)\)

\(\Rightarrow ab^2+abc=abc+b^2c\)

\(\Rightarrow ab^2=b^2c\)

\(\Rightarrow ab=bc\Rightarrow\frac{a}{b}=\frac{b}{c}\left(đpcm\right)\)