Question

Chứng minh \(\dfrac {a}{b} = \dfrac {c}{d}\) nếu biết

a, \(\dfrac {4a-3b}{a}=\dfrac {4c-3d}{c}\)

b, \(\dfrac {1111c-99d}{9999-11d} = \dfrac {1111a-99b}{9999a-11b}\)

Answer 1

a) \(\frac{4a-3b}{a}=\frac{4c-3d}{c}\Leftrightarrow4-\frac{3b}{a}=4-\frac{3d}{c}\)

\(\Leftrightarrow\frac{b}{a}=\frac{d}{c}\Leftrightarrow\frac{a}{b}=\frac{c}{d}\)

b) \(\frac{1111c-99d}{9999c-11d}=\frac{1111a-99b}{9999a-11b}\Leftrightarrow\frac{9\left(9999-11d\right)-88880c}{9999c-11d}=\frac{9\left(9999a-11b\right)-88880a}{9999a-11b}\)

\(\Leftrightarrow9+\frac{-88880c}{9999c-11d}=9+\frac{-88880a}{9999a-11b}\)

\(\Leftrightarrow\frac{c}{9999c-11d}=\frac{a}{9999a-11b}\)

\(\Leftrightarrow\frac{9999c-11d}{c}=\frac{9999a-11b}{a}\)

\(\Leftrightarrow9999-\frac{11d}{c}=9999-\frac{11b}{a}\Leftrightarrow\frac{d}{c}=\frac{b}{a}\Leftrightarrow\frac{c}{d}=\frac{a}{b}\)

câu b hình như đề sai