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

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

\(\Rightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)

 (Đpcm)

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

Áp dụng t/c dãy tỉ số bằng nhau : 

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

\(\Rightarrow5\left(b-6\right)=6\left(a-5\right)\Leftrightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)

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

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

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

\(\Leftrightarrow10b=12a\)

\(\Rightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\left(đpcm\right)\)

a+5/a-5=b+6/b-6=a+5/b+6=b+6/b-69 (giao hoán trung tỉ)=>(a+5)-5/(b+6)-6=(a+5)-a/(b+6)-6=a/b=5/6

BẠN ƠI CÁI MÀ '/' LÀ PHẦN NHA

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

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

\(\Rightarrow5b=6a\)

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

Đpcm

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

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

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

<=> \(\frac{10}{a-5}=\frac{12}{b-6}\)

<=> 10( b - 6 ) = 12( a - 5 )

<=> 5( b - 6 ) = 6( a - 5 )

<=> 5b - 30 = 6a - 30

<=> 5b = 6a

<=> \(\frac{6}{5}=\frac{b}{a}\)hay \(\frac{a}{b}=\frac{5}{6}\)( đpcm )

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

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

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

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

\(\Leftrightarrow5b+5b=6a+6a\)

\(\Leftrightarrow10b=12a\)

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

Ta có : \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{b-6}{a-5}=\frac{b+6}{a+5}\)

Áp dụng t/c dãy tỉ số bằng nhau : 

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

\(\Rightarrow5\left(b-6\right)=6\left(a-5\right)\Leftrightarrow5b-30=6a-30\Leftrightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)

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

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

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

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

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

nhân chéo là dễ nhất

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

\(=>ab-6a+5b-30=ab+6a-5b-30\) (phân phối)

=>-6a+5b=6a-5b

=>6a-(-6a)=5b-(-5b)

=>12a=10b

=>a/b=10/12=5/6 đpcm

Ta có: \(\frac{x+5}{x-5}=\frac{b+6}{b-6}\)

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

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

\(\Leftrightarrow16a=10b\)

\(\Leftrightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\left(đpcm\right)\)

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

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

\(\Leftrightarrow1+\frac{10}{a-5}=1+\frac{12}{b-6}\)

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

\(\Rightarrow10.\left(b-6\right)=12.\left(a-5\right)\)

\(10b-60=12a-60\)

\(10b=12a\)

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

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

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

\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{a+5+\left(a-5\right)}{b+6+\left(b-5\right)}=\frac{a+5+a-5}{b+6+b-6}=\frac{2a}{2b}=\frac{a}{b}\)

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

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

Ta có : \(\frac{a+5}{b-5}\frac{b+6}{b-6}\)

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

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

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

\(\frac{2a}{2b}=\frac{5.2}{6.2}=\frac{10}{12}\)

=> \(\frac{a}{b}=\frac{5}{6}\left(\text{đ}pcm\right)\)

Từ

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

Áp dụng tính chất của dãy tỉ số bằng nhau . Ta có

\(\frac{b-6}{a-5}=\frac{b+6}{a+5}=\frac{b-6+b+6}{a-5+a+5}=\frac{2b}{2b}=\frac{b}{a}=\frac{b+6-b}{a+5-a}=\frac{6}{5}\)

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

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