Question

cho \(\frac{a}{b}=\frac{c}{d}\) CMR 

a, \(\frac{c+d}{a+b}=\frac{c}{a}\)

b, \(\left(\frac{a-b}{c-d}\right)^{2013}=\frac{a^{2013}+b^{2013}}{c^{2013}+d^{2013}}\)

Answer 1

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

Áp dụng tính chất dãy tỉ số bằng nhau:

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

Answer 2

a) Ta có : \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{c}{a}=\frac{d}{b}=\frac{c+d}{a+b}\Rightarrow\frac{c+d}{a+b}=\frac{c}{a}\left(\text{đpcm}\right)\)

b)Ta có : \(\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\frac{a^{2013}}{c^{2013}}=\frac{b^{2013}}{d^{2013}}=\left(\frac{a-b}{c-d}\right)^{2013}=\frac{a^{2013}+b^{2013}}{c^{2013}+d^{2013}}\left(\text{đpcm}\right)\)