\(\dfrac{a}{6}=\dfrac{b}{9}\)

\(\Leftrightarrow9a=6b\)

\(\Rightarrow3a=2b\)(chia cả 2 vế cho 3)

\(\Rightarrow3a-2b=0\Rightarrow\dfrac{3a-2b}{3a+2b}=0\)

Chúc bn học tốt

Ta có: `a/6 = b/9` `-> 9a = 6b`

`-> 3a = 2b`

Vì `3a = 2b` nên `3a - 2b = 0`.

`-> A = (3a - 2b)/(3a + 2b) = 0/(3a + 2b) = 0` 

Vậy giá trị biểu thức `A` là `0`.

b

\(a;b>0\Rightarrow3a+2b+1>1\)

\(\Rightarrow log_{3a+2b+1}\left(9a^2+b^2+1\right)\) đồng biến

Mà \(9a^2+b^2\ge2\sqrt{9a^2b^2}=6ab\Rightarrow log_{3a+2b+1}\left(9a^2+b^2+1\right)\ge log_{3a+2b+1}\left(6ab+1\right)\)

\(\Rightarrow log_{3a+2b+1}\left(9a^2+b^2+1\right)+log_{6ab+1}\left(3a+2b+1\right)\ge log_{3a+2b+1}\left(6ab+1\right)+log_{6ab+1}\left(3a+2b+1\right)\ge2\)

Đẳng thức xảy ra khi và chỉ khi: \(\left\{{}\begin{matrix}log_{6ab+1}\left(3a+2b+1\right)=1\\3a=b\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}6ab+1=3a+2b+1\\b=3a\end{matrix}\right.\)

\(\Rightarrow18a^2+1=3a+6a+1\)

\(\Leftrightarrow18a^2-9a=0\Rightarrow\left\{{}\begin{matrix}a=\dfrac{1}{2}\\b=\dfrac{3}{2}\end{matrix}\right.\)

làm ơn trả lời hộ mk với ah mai mk phải nộp bài r

=4 nhé

nó bảo sai bạn ạ

chắc la sai ở chỗ nào rồi

Đặt \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=k\)

\(\rightarrow a=2k;b=3k;c=4k\)

\(M=\dfrac{3a+2b-4c}{8a-5b+2c}\\ =\dfrac{3.2k+2.3k-4.4k}{8.2k-5.3k+2.4k}\\ =\dfrac{6k+6k-8k}{16k-15k+8k}\\ =\dfrac{4k}{9k}=\dfrac{4}{9}\)

Vậy \(M=\dfrac{4}{9}\)

Đặt \(\frac{a}{2}=\frac{b}{-3}=\frac{c}{-4.5}=k\) suy ra \(a=2k,b=-3k;c=-4,5k\)

Thay vào P ,ta có:  \(P=\frac{3.2k-\left(-3k.2\right)}{8.2k+3k+\left(-4,5k\right)}=\frac{6k+6k}{16k+3k-4,5k}=\frac{12k}{14.5k}=\frac{12}{14.5}=\frac{24}{29}\)

Vậy ...

ta có 

\(A=\frac{3a-2b}{2a-3b}=\frac{\frac{3a}{b}-2}{\frac{2a}{b}-3}=\frac{\frac{3.5}{6}-2}{\frac{2.5}{6}-3}=\frac{\frac{1}{2}}{-\frac{4}{3}}=-\frac{3}{2}\)

a-b=7 nên a=b+7

\(P=\dfrac{3\left(b+7\right)-b}{2\left(b+7\right)+7}+\dfrac{3b-b-7}{2b-7}=1+1=2\)