Question

Chỉ tỉ lệ thức a/b=c/d.hay chung minh 5a+3b / 5a-3b=5c+3d / 5c - 3d

chứng minh = cách đặt k nha ?

Answer 1

Đặt \(\frac{a}{b}=\frac{c}{d}=k=>a=bk,c=dk\)

=>\(\frac{5a+3b}{5a-3b}=\frac{5.bk+3b}{5.bk-3b}=\frac{5.bk-3b+3b+3b}{5.bk-3b}=1+\frac{6b}{\left(5k-3\right).b}=1+\frac{6}{5k-3}\)

\(\frac{5c+3d}{5c-3d}=\frac{5.dk+3d}{5.dk-3d}=\frac{5.dk-3d+3d+3d}{5.dk-3d}=1+\frac{6d}{\left(5k-3\right).d}=1+\frac{6}{5k-3}\)

=>\(\frac{5a+3b}{5a-3b}=1+\frac{6}{5k-3}=\frac{5c+3d}{5c-3d}\)

=>\(\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}\)