Question

Answer 1

ta có : `a/b=c/d=>a.d=b.c`

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

`=>(5a+3b).(5c-3d)=(5a-3b).(5c+3d)`

`=>25ac - 15ad + 15bc - 9bd= 25ac +15ad -15bc - 9bd`

vậy `a/b=c/d` thì `(5a+3b)/(5a-3b)=(5c+3d)/(5c-3d`

Answer 2

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

Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:

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

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