Question

Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) \(\left(a\ne5,b\ne6\right)\). Như vậy tỉ số \(\frac{a}{b}\) bằng .....

Answer 1

\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right).\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)

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

\(\Rightarrow\left(ab-6a+5b-30\right)-\left(ab+6a-5b-30\right)=0\)

\(\Rightarrow ab-6a+5b-30-ab-6a+5b+30=0\)

\(\Rightarrow-12a+10b=0\)

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

Answer 2

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

\(\Rightarrow5a-6b=6a-5b\)

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

\(-a=b\)

\(\frac{a}{b}=-1\)

Answer 3

a/b = 5/6.

Answer 4

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

\(\Rightarrow a.b+5.b-6a-30\)

\(=a.b-5.b+6.a-30\)

\(\Rightarrow a.b+10.b=a.b+12a\)

\(\Rightarrow10.b=12a\Rightarrow5.b=6.a\Rightarrow\frac{a}{b}=\frac{5}{6}\)(đpcm)