Question

Chứng minh rằng nếu \(\frac{a}{b}=\frac{c}{d}\) thì \(\frac{2a-3b}{2a+3b}=\frac{2c-3d}{2c+3d}\)

Answer 1

đặt : \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=b.k;c=d.k\) 

Ta có :\(\frac{2a-3b}{2a+3b}=\frac{2.b.k-3b}{2.b.k+3b}=\frac{b\left(2k-3\right)}{b\left(2k+3\right)}=\frac{2k-3}{2k+3}\)

                                                                            \(=\)   \(\frac{d\left(2k-3\right)}{d\left(2k+3\right)}=\frac{2d.k-3d}{2.d.k+3d}=\frac{2c-3d}{2c+3d}\left(c=d.k\right)\)

Answer 2

Đặt a / b = c/d = K . Suy ra :

a = b.K ; c = d.K

Ta có: 2a-3b/2a+3b = 2.b.K-3b/2.b.K+3b =b(2.k-3)/ b(2.k+3) = 2k-3/2k+3     (1)

          2c-3d/2c+3b = 2.d.k-3d/2.d.k+3d = d(2.k-3)/d(2.k+3) = 2k-3/2k+3      (2)

Từ (1) và (2) . Suy ra : 2a-3b/2a+3b = 2c-3d/2c+3d