Cho a + 5/a - 5 = b + 6/b - 6. (a khác 5, b khác 6). Chứng minh a/b = 5/6

Lời giải

\(\frac{{a + 5}}{{a - 5}} = \frac{{b + 6}}{{b - 6}}\)

\(\frac{{a - 5}}{{a - 5}} + \frac{{10}}{{a - 5}} = \frac{{b - 6}}{{b - 6}} + \frac{{12}}{{b - 6}}\)

\(1 + \frac{{10}}{{a - 5}} = 1 + \frac{{12}}{{b - 6}}\)

\(\frac{{10}}{{a - 5}} = \frac{{12}}{{b - 6}}\)

\( \Rightarrow 12(a - 5) = 10(b - 6)\)

\( \Rightarrow 6(a - 5) = 5(b - 6)\)

\( \Rightarrow \)6a – 30 = 5b – 30

\( \Rightarrow \)6a = 5b

\( \Rightarrow \)\(\frac{a}{b} = \frac{5}{6}\)