Question

cho\(\dfrac{a+5}{a-5}=\dfrac{b+6}{b-6}\)(a\(\ne\)5;b\(\ne\)6) chứng minh:\(\dfrac{a}{b}=\dfrac{5}{6}\)

Answer 1

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

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

\(\Rightarrow ab+5b-6a-30=ab-5b+6a-30\)

\(\Rightarrow5b-6a=-5b+6a\)

\(\Rightarrow10b=12a\)

\(\Rightarrow5b=6a\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{5}{6}\left(đpcm\right)\)

Vậy \(\dfrac{a}{b}=\dfrac{5}{6}\)

Answer 2

\(\dfrac{a+5}{a-5}=\dfrac{a+6}{a-6}\)suy ra \(\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(a+6\right)\)

suy ra: \(6a=5b\)

suy ra: \(\dfrac{a}{b}=\dfrac{5}{6}\)

Answer 3

Một cách giải khác:

TH1: b = -6

VP = 0 => VT = 0 => a = -5

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

TH2: b \(\ne\) -6 nên:

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

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

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