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)

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Câu a

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

Vậy chọn B

b

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

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

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

\(\Rightarrow6a+30=5a-25\)

\(\Rightarrow6a-5a=-25-30\)

\(\Rightarrow a=-55\)

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

\(\Rightarrow6b+36=5b-30\)

\(\Rightarrow6b-5b=-30-36\)

\(\Rightarrow b=-66\)

\(\Rightarrow\frac{a}{b}=\frac{-55}{-66}=\frac{5}{6}\left(đpcm\right)\)

Ta co a+5/a-5=b+6/b-6

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

<=> 6a=5b

<=> a/b=5/6

,

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

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

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

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

\(\Rightarrow12\left(a-5\right)=10\left(b-6\right)\)

\(\Rightarrow6\left(a-5\right)=5\left(b-6\right)\)

\(\Rightarrow6a-30=5b-30\)

\(\Rightarrow6a=5b\)

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

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

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 )

Ta có: \(\dfrac{a+5}{a-5}\)=\(\dfrac{b+6}{b-6}\) --->\(\dfrac{a-5+5+5}{a-5}\)=\(\dfrac{b-6+6=6}{b-6}\)

\(\dfrac{\left(a-5\right)+10}{a-5}\)= \(\dfrac{\left(b-6\right)+12}{b-6}\)--> 1+\(\dfrac{10}{a-5}\)=1+\(\dfrac{12}{b-6}\)

---> \(\dfrac{10}{a-5}\)= \(\dfrac{12}{b-6}\)---> \(\dfrac{b-6}{a-5}\)=\(\dfrac{12}{10}\)=\(\dfrac{6}{5}\)

--> 5.( b-6)= 6.(a-5) ---> 5b- 30= 6a- 30

---> 5b = 6a--->\(\dfrac{a}{b}\) =\(\dfrac{5}{6}\)( Đpcm)

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