Question

Chứng minh tỉ lệ thức sau

Cho a/b=c/d

CM: a/3a+b=c/3c+d

Answer 1

Xét \(\frac{a}{b}=k;\frac{c}{d}=k\)

=> a= bk; c= dk

Thay:

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

\(\frac{c}{3c+d}=\frac{dk}{3.dk+d}=\frac{dk}{3.d\left(k+1\right)}=\frac{k}{3.\left(k+1\right)}\) (2)

Ta thấy (1)= (2)

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

Answer 2

theo bài ra ta có:

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{3a}{3c}\)

áp dụng t/c dãy tỉ số bằng nhau ta có:

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

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

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