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\(\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Leftrightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Leftrightarrow ab-ab+5b+5b-30+30=6a+6a\)
\(\Leftrightarrow10b=12a\)
\(\Rightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\left(đpcm\right)\)
- \(\frac{a+5}{a-5}\)=\(\frac{b+6}{b-6}\)(ta hoán đổi trung tỉ)=>\(\frac{a+5}{b+6}\)=\(\frac{a-5}{b-6}\)=>\(\frac{\left(a+5\right)-5}{\left(b+6\right)-6}\)=\(\frac{\left(a+5\right)-a}{\left(b+6\right)-b}\)=a/b=5/6
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
<=> \(\frac{a-5+10}{a-5}=\frac{b-6+12}{b-6}\)
<=> \(1+\frac{10}{a-5}=1+\frac{12}{b-6}\)
<=> \(\frac{10}{a-5}=\frac{12}{b-6}\)
<=> 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 )
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: \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Rightarrow\left(a+5\right).\left(b-6\right)=\left(a-5\right).\left(b+6\right)\)
\(ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow5b-6a=6a-5b\)
\(5b+5b=6a+6a\)
\(10b=12a\)
\(\Rightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\)
Vậy \(\frac{a}{b}=\frac{5}{6}\)
Tham khảo nhé~
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right).\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow\left(ab-6a+5b-30\right)-\left(ab+6a-5b-30\right)=0\)
\(\Rightarrow ab-6a+5b-30-ab-6a+5b+30=0\)
\(\Rightarrow-12a+10b=0\)
\(\Rightarrow-12a=10b\Rightarrow\frac{a}{b}=\frac{-10}{12}\Rightarrow\frac{a}{b}=\frac{-5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow ab+5b-6a-30=ab+6a-5b-30\)
\(\Rightarrow5a-6b=6a-5b\)
\(5a-6a=-5b+6b\)
\(-a=b\)
\(\frac{a}{b}=-1\)
Bài giải
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Rightarrow\text{ }\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{\left(a+5\right)+\left(a-5\right)}{\left(b+6\right)+\left(b-6\right)}=\frac{2a}{2b}=\frac{a}{b}=\frac{\left(a+5\right)-\left(a-5\right)}{\left(b+6\right)-\left(b-6\right)}=\frac{10}{12}=\frac{5}{6}\)
( Áp dụng tính chất của dãy tỉ số bằng nhau )
\(\Rightarrow\text{ }\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow5b=6a\)
\(\Rightarrow\frac{a}{b}=\frac{5}{6}\)
Đpcm