Ta có:

\(\frac{2a}{3}=\frac{3b}{4}\Rightarrow\frac{2a}{3}:6=\frac{3b}{4}:6\)

\(\Rightarrow\frac{a}{9}=\frac{b}{8}\Rightarrow\frac{a}{27}=\frac{b}{24}\) ( 1 )

\(\frac{1}{4}\left(2b\right)=\frac{1}{5}\left(-3c\right)\Rightarrow\frac{b}{2}=\frac{-3c}{5}\Rightarrow\frac{b}{2}:3=-\frac{3c}{5}:3\)

\(\Rightarrow\frac{b}{6}=\frac{c}{-5}\Rightarrow\frac{b}{24}=\frac{c}{-20}\) (2 )

Từ (1) và ( 2) có:

\(\frac{a}{27}=\frac{b}{24}=\frac{c}{-20}\)

\(\Rightarrow\frac{a}{27}=\frac{2b}{48}=\frac{3c}{-60}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{a}{27}=\frac{2b}{48}=\frac{3c}{-60}=\frac{a-2b+3c}{27-48+\left(-60\right)}=\frac{1}{-81}\)

\(\Rightarrow\frac{a}{27}=\frac{b}{24}=\frac{c}{-20}=-\frac{1}{81}\)

\(\Rightarrow a-b-c=-\frac{1}{81}\left[27-24-\left(-20\right)\right]=-\frac{1}{81}.23=-\frac{23}{81}\)

bạn ghi lại đề đi bạn

đặt a/b =c/d =k 

=> a=bm , c=dm 

=> 2a+3c/2b+3d =2bm+3bm/ 2b +3d = m.(2d+3d)/2d+3d =m (1)

=> 2a-3c/2d-3d=2bm-3dm /2b -3d =m.(2b-3d)/2b-3d= m (2)

Từ (1) và (2) => 2a+3c/2b+3d =2a-3c/2b-3d 

câu 2 tương tự nha

bạn khôi đặt là k mà lại khi m

Ta có: a, b, c tỉ lệ với 2, 3, 5

\(\Rightarrow\frac{a}{2}=\frac{b}{3}=\frac{c}{5}.\)

Đặt \(\frac{a}{2}=\frac{b}{3}=\frac{c}{5}=k\Rightarrow\left\{{}\begin{matrix}a=2k\\b=3k\\c=5k\end{matrix}\right.\)

Có: \(A=\frac{a+2b-c}{a-2b+3c}.\)

\(\Rightarrow A=\frac{2k+2.3k-5k}{2k-2.3k+3.5k}\)

\(\Rightarrow A=\frac{2k+6k-5k}{2k-6k+15k}\)

\(\Rightarrow A=\frac{\left(2+6-5\right).k}{\left(2-6+15\right).k}\)

\(\Rightarrow A=\frac{3k}{11k}\)

\(\Rightarrow A=\frac{3}{11}.\)

Vậy \(A=\frac{3}{11}.\)

Chúc bạn học tốt!

Ta có :

\(\frac{a}{b}=\frac{5}{6}\Rightarrow\frac{a}{b}=\frac{20}{24}\Rightarrow\frac{a}{20}=\frac{b}{24}\)\(\left(1\right)\)

\(\frac{b}{c}=\frac{8}{9}\Rightarrow\frac{b}{c}=\frac{24}{27}\Rightarrow\frac{b}{24}=\frac{c}{27}\)\(\left(2\right)\)

\(\frac{c}{d}=\frac{3}{2}\Rightarrow\frac{c}{d}=\frac{27}{18}\Rightarrow\frac{c}{27}=\frac{d}{18}\)\(\left(3\right)\)

Từ ( 1 ) ; ( 2 ) ; ( 3 ) \(\Rightarrow\frac{a}{20}=\frac{b}{24}=\frac{c}{27}=\frac{d}{18}=\frac{d-c}{18-24}=\frac{54}{-6}=-9\)

\(\frac{a}{20}=-9\Rightarrow a=-9.20=-180\)

\(\frac{b}{24}=-9\Rightarrow b=-9.24=-216\)

\(\frac{c}{27}=-9\Rightarrow c=-9.27=-243\)

\(\frac{d}{18}=-9\Rightarrow d=-9.18=-162\)

\(\Rightarrow A=a+2b+3c+4d=-180+\left(-216\right).2+\left(-243\right).3+\left(-162\right).4\)

\(=-1989\)

a ; b ;c tỉ lệ với 2;3;4 

=> \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}\)

=> \(\frac{a}{2}=\frac{2b}{6}=\frac{3b}{12}=\frac{a+2b+3b}{2+6+12}=\frac{-20}{20}=-1\)

=> a = -1.2 = -2

=> b= -1.3= -3

=> c= -1 . 4 = -4

Có a; b; c tỉ lậ với 2; 3; 4

=> \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}\)

=> \(\frac{a}{2}=\frac{2b}{6}=\frac{3c}{12}=\frac{a+2b+3c}{2+6+12}=\frac{-20}{20}=-1\)

=> a = (-1).2 = -2

     2b = (-1).6 = (-6) => b = -3

     3c = (-1).12 = (-12) => c = -4

KL: a = -2; b = -3; c = -4

ta có :

\(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=>\frac{a}{2}=\frac{2b}{6}=\frac{3c}{12}\)

áp dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{a}{2}=\frac{2b}{6}=\frac{3c}{12}=\frac{a+2b+3c}{2+6+12}=-\frac{20}{20}=-1\)

=>a/2=-1=>a=-2

=>b/3=-1=>b=-3

=>c/4=-1=>c=-4

sai đề r, a/3 là s, phải a/b chứ, nếu là a/b thì lm ntnày:

Lấy a/b=c/d=k(k thuộc N*) 
=>a=bk ; c=dk 
Xét : + 2a-3c/2b-3d=2bk-3dk/2b-3d= k^2.(2b-3d)/2b-3d=k^2 (1) 
       + 2a+3c/2b+3d=2bk+3dk/2b+3d= k^2.(2b+3d)/2b+3d=k^2 (2) 
(1);(2)=> 2a-3c/2b-3d=2a+3c/2b+3d(đpcm)

Vậy 2a-3c/2b-3d=2a+3c/2b+3d

Đặt:

\(\dfrac{a}{10}=\dfrac{b}{8}=\dfrac{c}{6}=t\Leftrightarrow\left\{{}\begin{matrix}a=10t\\b=8t\\c=6t\end{matrix}\right.\)

\(M=\dfrac{a+2b-3c}{a-2b+3c}=\dfrac{10t+16t-18t}{10t-16t+18t}=\dfrac{8t}{12t}=\dfrac{8}{12}=\dfrac{2}{3}\)