Ta có: \(\frac{2a+b}{a-b}=\frac{2c+d}{c-d}.\)
\(\Rightarrow\left(2a+b\right).\left(c-d\right)=\left(2c+d\right).\left(a-b\right)\)
\(\Rightarrow2a.\left(c-d\right)+b.\left(c-d\right)=2c.\left(a-b\right)+d.\left(a-b\right)\)
\(\Rightarrow2ac-2ad+bc-bd=2ac-2bc+ad-bd\)
\(\Rightarrow2ad+bc-bd=2bc+ad-bd\)
\(\Rightarrow2ad+bc=2bc+ad.\)
\(\Rightarrow2ad-ad=2bc-bc\)
\(\Rightarrow ad=bc\)
\(\Rightarrow\frac{a}{b}=\frac{c}{d}\left(đpcm\right).\)
Chúc em học tốt!
cho \(\frac{2a+b}{a-2b}=\frac{2c+d}{c-2d}\)c/m rang \(\frac{a}{b}=\frac{c}{d}\)
Cho dãy tỉ số bằng nhau:
\(\frac{2a+b+c+d}{a}=\frac{a+2b+c+d}{b}=\frac{a+b+2c+d}{c}=\frac{a+b+c+2d}{d}\)
Tính: \(M=\frac{a+b}{c+d}+\frac{b+c}{d+a}+\frac{c+d}{a+b}+\frac{d+a}{b+c}\)
Cho dãy tỉ số bằng nhau :
\(\frac{2a+b+c+d}{a}=\frac{a+2b+c+d}{b}=\frac{a+b+2c+d}{c}=\frac{a+b+c+2d}{d}\)
Tính \(M=\frac{a+b}{c+d}+\frac{b+c}{d+a}+\frac{c+d}{a+b}+\frac{d+a}{b+c}\)
a) cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
i) \(\frac{a}{a+b}\frac{c}{c+d}\)
ii)\(\frac{a-b}{c-d}=\frac{a+c}{b+d}.\)
b) Cho: \(\frac{2a+b}{a-2b}=\frac{2c+d}{c-2d}\). Chứng minh: \(\frac{a}{b}=\frac{c}{d}.\)
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh: \(\left(\frac{a-b}{c-d}\right)^{^{2019}}=\frac{2a^{2019}-b^{2019}}{2c^{2019}-d^{2019}}\)
Câu 1: Cho dãy tỉ số bằng nhau:
\(\frac{2a+b+c+d}{a}=\frac{a+2b+c+d}{b}=\frac{a+b+2c+d}{c}=\frac{a+b+c+2d}{d}\)
Tính M = \(\frac{a+b}{c+d}+\frac{b+c}{d+a}+\frac{c+d}{a+b}+\frac{d+a}{b+c}\)
Câu 2: Chứng minh rằng:
A= 75.(42004+42003+.....+42+4+1)+25 là số chia hết cho 100
cho\(\frac{a}{b}=\frac{c}{d}\) chứng minh rằng:
a, \(\frac{2a+3b}{3a-4b}=\frac{2c+3d}{3c-4d}\)
b, \(\frac{2a^2-3ab+4b^2}{2b^2+5ab}=\frac{2c^2-3cd+4d^2}{2d^2+5cd}\)
cho \(\frac{a}{b}=\frac{c}{d}\)\(\left(c\ne\pm d\right)\) . chứng minh
a, \(\frac{2a+7b}{2a-7b}=\frac{2b+7d}{2c-7d}\)
b, \(\frac{5a^2+7ab}{9a^2-11b^2}=\frac{5c^2+7cd}{9c^2-11d^2}\)
