Toán Lớp 7: `cho x/y = m/n . chứng minh 2x+3y / 2x-3y = 2m+3n / 2m-3n`

Question

Toán Lớp 7:  cho  x/y = m/n . chứng minh 2x+3y / 2x-3y = 2m+3n / 2m-3n

hienchaudiem · Answer

Giải đáp:   $  $   Đặt x/y = m/n = k   &harr;   ( left {  begin{array}{l} dfrac{x}{y}=k    dfrac{m}{n}=k end{array}  right. )     &harr;  ( left {  begin{array}{l}x=yk  m=nk end{array}  right. )     C&oacute; : (2x+ 3y)/(2x - 3y)     = (2yk + 3y)/(2yk -3y)     = (y (2k + 3) )/(y (2k -3) )     = (2k + 3)/(2k-3) (1)     C&oacute; : (2m+3n)/(2m-3n)     = (2nk + 3n)/(2nk-3n)     = (n (2k+3) )/(n (2k-3) )     = (2k+3)/(2k-3) (2)     Từ (1), (2)     -> (2x+3y)/(2x-3y) = (2m+3n)/(2m-3n) (= (2k+3)/(2k-3) )     -> đpcm

ngochuong2k2 · Answer

~ Bạn tham khảo ~    Đặt x/y=m/n=k   => x=yk;m=nk    Thay v&agrave;o ta c&oacute; :    [2x+3y]/[2x-3y]=[2yk+3y]/[2yk-3y]=[y(2k+3)]/[y(2k-3)]=[2k+3]/[2k-3] (1)   [2m+3n]/[2m-3n]=[2nk+3n]/[2nk-3n]=[n(2k+3)]/[n(2k-3)]=[2k+3]/[2k-3] (2)   Từ (1),(2)=> [2x+3y]/[2x-3y]=[2m+3n]/[2m-3n] (Đpcm)