Question

[Trần Ngọc Hạnh Nguyên]

Cho \(\dfrac{a+4}{a-4}=\dfrac{b+5}{b-5}\) (a ≠ 4; b ≠ 5). Chứng minh \(\dfrac{a}{b}=\dfrac{4}{5}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\dfrac{a+4}{a-4}=\dfrac{b+5}{b-5}\)

=>\(\left(a+4\right)\left(b-5\right)=\left(a-4\right)\left(b+5\right)\)

\(\Leftrightarrow ab-5a+4b-20=ab+5a-4b-20\)

\(\Leftrightarrow-10a=-8b\)

=>a/b=4/5