Question

Cho \(\frac{a}{b}\)=\(\frac{c}{d}\)CMR :\(\frac{2005a-2006b}{2006a+2007b}=\frac{2005c-2006d}{2006c+2007d}\)

Answer 1

  Ta có: \(\frac{a}{b}=\frac{c}{d}\)=> \(\frac{a}{c}=\frac{b}{d}=\frac{2005a}{2005c}=\frac{2006b}{2006d}=\frac{2006a}{2006c}=\frac{2007b}{2007d}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{2005a}{2005c}=\frac{2006b}{2006d}=\frac{2006a}{2006c}=\frac{2007b}{2007d}=\frac{2005a-2006b}{2005c-2006d}=\frac{2006a+2007b}{2006c+2007d}\)

=> \(\frac{2005a-2006b}{2006c+2007d}=\frac{2005c-2006d}{2006a+2007b}\)