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a: \(\dfrac{a+5}{a-5}=\dfrac{b+6}{b-6}\)
=>(a+5)(b-6)=(a-5)(b+6)
=>ab-6a+5b-30=ab+6a-5b-30
=>-6a+5b=6a-5b
=>-12a=-10b
=>6a=5b
=>\(\dfrac{a}{b}=\dfrac{5}{6}\)
b: Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)
=>\(a=bk;c=dk\)
\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{b^2k^2+b^2}{d^2k^2+d^2}=\dfrac{b^2\left(k^2+1\right)}{d^2\left(k^2+1\right)}=\dfrac{b^2}{d^2}\)
\(\dfrac{ab}{cd}=\dfrac{bk\cdot b}{dk\cdot d}=\dfrac{b^2k}{d^2k}=\dfrac{b^2}{d^2}\)
Do đó: \(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(=\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{a+5-a+5}{b+6-b+6}=\frac{10}{12}=\frac{5}{6}\)
\(\Rightarrow\frac{a+5}{a-5}=\frac{5}{6}\)
\(\Rightarrow6a+30=5a-25\)
\(\Rightarrow6a-5a=-25-30\)
\(\Rightarrow a=-55\)
\(\Rightarrow\frac{b+6}{b-6}=\frac{5}{6}\)
\(\Rightarrow6b+36=5b-30\)
\(\Rightarrow6b-5b=-30-36\)
\(\Rightarrow b=-66\)
\(\Rightarrow\frac{a}{b}=\frac{-55}{-66}=\frac{5}{6}\left(đpcm\right)\)
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\(\dfrac{a+5}{a-5}=\dfrac{b+6}{b-6}\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(b+6\right)\left(a-5\right)\)
nhân ra ik ròi suy ra đpcm :D
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\frac{a-5}{a-5}+\frac{10}{a-5}=\frac{b-6}{b-6}+\frac{12}{b-6}\)
\(1+\frac{10}{a-5}=1+\frac{12}{b-6}\)
\(\frac{10}{a-5}=\frac{12}{b-6}\)
\(\Rightarrow12\left(a-5\right)=10\left(b-6\right)\)
\(\Rightarrow6\left(a-5\right)=5\left(b-6\right)\)
\(\Rightarrow6a-30=5b-30\)
\(\Rightarrow6a=5b\)
\(\Rightarrow\frac{a}{b}=\frac{5}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Leftrightarrow\left(a+5\right).\left(b-6\right)=\left(a-5\right).\left(b+6\right)\)
\(\Leftrightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Leftrightarrow12a=10b\)
\(\Leftrightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\left(dpcm\right)\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(b+6\right)\left(a-5\right)\)
\(\Leftrightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Leftrightarrow ab-6a+5b-30-ab-6a+5b+30=0\)
\(\Leftrightarrow-12a+10b=0\)
\(\Leftrightarrow-\frac{b}{12}=-\frac{a}{10}\)
\(\Leftrightarrow\frac{b}{12}=\frac{a}{10}\)
Tự lm tiếp
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
=> (a + 5)(b - 6) = (a - 5)(b + 6)
=> ab - 6a + 5b - 30 = ab + 6a - 5b - 30
=> -6a + 5b = 6a - 5b
=> 10b = 12a
=> 5b = 6a
=> \(\frac{a}{b}=\frac{5}{6}\)(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
<=> 5/6 = a/b ( đpcm )
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{a+5}{a-5}=\dfrac{b+6}{b-6}\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\\ \Leftrightarrow ab-6a+5b-30=ab+6a-5b-30\\ \Leftrightarrow12a=10b\\ \Leftrightarrow6a=5b\Leftrightarrow\dfrac{a}{b}=\dfrac{5}{6}\)
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) (a khác 5, b khác 6). Chứng minh \(\frac{a}{b}=\frac{5}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}=>\frac{a+5}{b+6}=\frac{a-5}{b-6}=>\frac{a}{b}=\frac{5}{6}\)