Question

3. CMR : Nếu \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) thì :

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

b) \(\dfrac{7a^2+3ab}{11a^2-8b^2}\)=\(\dfrac{7c^2+3ab}{11c^2-8d^2}\)

Answer 1

a)Đặt \(\dfrac{a}{b}=\dfrac{c}{b}=k\left(k\ne0\right)\)

=> a=bk; c=dk

+) \(\dfrac{5a+3b}{5a-3b}=\dfrac{5bk+3b}{5bk-3b}=\dfrac{b\left(5k+3\right)}{b\left(5k-3\right)}=\dfrac{5k+3}{5k-3}\left(1\right)\)

+) \(\dfrac{5c+3d}{5c-3d}=\dfrac{5dk+3d}{5dk-3d}=\dfrac{d\left(5k+3\right)}{d\left(5k-3\right)}=\dfrac{5k+3}{5k-3}\left(2\right)\)

Từ (1) và (2)=> \(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)

b) cũng đặt và cm tương tự