Question

cho \(\dfrac{a+5}{a-5}=\dfrac{b+6}{b-6}\) ( \(a\ne5;b\ne6\)). Chứng minh \(\dfrac{a}{b}=\dfrac{5}{6}\)

bạn nào biết làm ơn viết lời giải ra hộ mình với

Answer 1

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

\(\Rightarrow\left(a+5\right)\left(b-6\right)=\left(b+6\right)\left(a-5\right)\)

ab-6a+5b-30=ab-5b+6a-30

12a=10b

\(\dfrac{a}{b}=\dfrac{5}{6}\)

Answer 2

ta có :\(\dfrac{a+5}{a-5}=\dfrac{b+6}{b-6}\)\(=>\dfrac{a+5}{b+6}=\dfrac{a-5}{b-6}=\dfrac{a+5+a-5}{b+6+b-6}=\dfrac{2a}{2b}=\dfrac{a}{b}\left(1\right)\)

Mặt khác:\(\dfrac{a+5}{b+6}=\dfrac{a-5}{b-6}=\dfrac{a+5-a+5}{b+6-b+6}=\dfrac{10}{12}=\dfrac{5}{6}\left(2\right)\) Từ (1),(2)=>\(\dfrac{a}{b}=\dfrac{5}{6}\left(đpcm\right)\)

Answer 3

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

⇔\(\left(a+5\right)\cdot\left(b-6\right)=\left(a-5\right)\cdot\left(b+6\right)\)

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

Vậy \(\frac{a}{b}=\frac{5}{6}\)