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\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\frac{a-5}{a-5}+\frac{10}{a-5}=\frac{b-6}{b-6}+\frac{12}{b-6}\)
\(1+\frac{10}{a-5}=1+\frac{12}{b-6}\)
\(\frac{10}{a-5}=\frac{12}{b-6}\)
\(\Rightarrow12\left(a-5\right)=10\left(b-6\right)\)
\(\Rightarrow6\left(a-5\right)=5\left(b-6\right)\)
\(\Rightarrow6a-30=5b-30\)
\(\Rightarrow6a=5b\)
\(\Rightarrow\frac{a}{b}=\frac{5}{6}\)
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) (a khác 5, b khác 6). Chứng minh \(\frac{a}{b}=\frac{5}{6}\)
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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)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)
(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 :
\(\frac{b-6}{a-5}=\frac{b+6}{a+5}=\frac{\left(b+6\right)-\left(b-6\right)}{\left(a+5\right)-\left(a-5\right)}=\frac{12}{10}=\frac{6}{5}\)
\(\Rightarrow5\left(b-6\right)=6\left(a-5\right)\Leftrightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Vì \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{a+5}{b+6}=\frac{a-5}{b-6}\)
Áp dụng TC DTSBN ta có :
\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{\left(a+5\right)+\left(a-5\right)}{\left(b+c\right)+\left(b-6\right)}=\frac{2a}{2b}=\frac{a}{b}\) (1)
\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{\left(a+5\right)-\left(a-5\right)}{\left(b+6\right)-\left(b-6\right)}=\frac{10}{12}=\frac{5}{6}\)(2)
Từ (1) ; (2) \(\Rightarrow\frac{a}{b}=\frac{5}{6}\)(đpcm)
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\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\Rightarrow a.b+5.b-6a-30=a.b-5.b+6.a-30\Rightarrow a.b+10.b=a.b+12a\)\(\Rightarrow10.b=12.a\Rightarrow5.b=6.a\Rightarrow\frac{a}{b}=\frac{5}{6}\left(đpcm\right)\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
=> 6a = 5b
=> \(\frac{a}{b}=\frac{5}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) => (a + 5)(b - 6) = (a - 5)(b + 6) => ab - 6a + 5b - 30 = ab + 6a - 5b - 30
=>\(-6a+5b\) = 6a - 5b =\(-\left(6a-5b\right)\) => 6a - 5b = 0 => 6a = 5b => \(\frac{a}{b}=\frac{5}{6}\)(đpcm)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{2a}{2b}=\frac{a}{b}\)
Suy ra:\(\frac{a+5}{b+6}=\frac{a}{b}\Rightarrow a.\left(b+6\right)=b.\left(a+5\right)\)
=>ab+6a=ab+5b
=>6a=5b
=>\(\frac{a}{b}=\frac{5}{6}\)
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Từ a+5/a-5=b+6/b-6
=>a+5/b+6=a-5/b-6
Áp dụng.... ta có:
a+5/b+6=a-5/b-6=(a+5+a-5)/(b+6+b-6)
=2a/2b=a/b. (1)
Vì a+5/b+6=a/b
Áp dụng.. ta có
a+5/b+6=a/b=a+5-a/b+6-b=5/6 (2)
Từ (1),(2)=>a/b=5/6(đpcm)
Tick nhé ,bài đúng 100%
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{a+5}{b+6}=\frac{a-5}{b-6}\Rightarrow\frac{a}{b}=\frac{5}{6}\)
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\(\frac{a+2015}{a-2015}=\frac{b+2016}{b-2016}\Rightarrow\)\(\frac{a+2015}{a-2015}-1=\frac{b+2016}{b-2016}-1\)
\(\frac{a+2015-a+2015}{a-2015}=\frac{b+2016-b+2016}{b-2016}\Rightarrow\)\(\frac{2015}{a-2015}=\frac{2016}{b-2016}\Rightarrow\)
2015(b-2016) =2016(a-2015) =>2015b =2016a =>\(\frac{a}{b}=\frac{2015}{2016}\)