\(\frac{a+b}{c}=\frac{b+c}{a}=\frac{c+a}{b}\)

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

\(\frac{a+b}{c}=\frac{b+c}{a}=\frac{c+a}{b}=\frac{a+b+b+c+c+a}{a+b+c}=\frac{2\left(a+b+c\right)}{a+b+c}=2\)

Vậy ...... 2

\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\left(-\frac{3}{2}\right)+\frac{2}{5}\right|\)

\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\frac{11}{10}\)

\(\left|x-\frac{1}{3}\right|=\frac{3}{10}\)

\(\Rightarrow\hept{\begin{cases}x-\frac{1}{3}=\frac{3}{10}\\x-\frac{1}{3}=-\frac{3}{10}\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{19}{30}\\x=\frac{1}{30}\end{cases}}}\)

Vậy..........

dddddddd

\(a^2=bc\Rightarrow\frac{a}{b}=\frac{c}{a}\Leftrightarrow\frac{a}{c}=\frac{b}{a}=\frac{a+b}{a+c}=\frac{a-b}{c-a}\Leftrightarrow\frac{a+b}{a-b}=\frac{c+a}{c-a}\)

Đặt \(A=2\left|2x-1\right|-3\left|2x+3\right|\)

TH1 : \(x< -\frac{3}{2};\) ta có :

\(A=2.\left(1-2x\right)-3.\left[-\left(2x+3\right)\right]\)

\(=2-4x+6x+9\)

\(=2x+11\)

TH2 : \(-\frac{3}{2}\le x< \frac{1}{2};\)ta có :

\(A=2\left(1-2x\right)-3\left(2x+3\right)\)

\(=2-4x-6x-9\)

\(=-10x-7\)

TH3 : \(x\ge\frac{1}{2};\)ta có :

\(A=2\left(2x-1\right)-3\left(2x+3\right)\)

\(=4x-2-6x-9\)

\(=-2x-11\)

+ Với \(x< -\frac{3}{2}\) thì |2x - 1| = 1 - 2x; |2x + 3| = -(2x + 3) = -2x - 3

Ta có: 2.|2x - 1| - 3.|2x - 3| = 2.(1 - 2x) - 3.(-2x - 3)

= 2 - 4x + 6x + 9

= 2x + 11

+ Với \(-\frac{3}{2}\le x< \frac{1}{2}\) thì |2x - 1| = 1 - 2x; |2x + 3| = 2x + 3

Ta có: 2.|2x - 1| - 3.|2x + 3| = 2.(1 - 2x) - 3.(2x + 3)

= 2 - 4x - 6x - 9

= -10x - 7

+ Với \(x>\frac{1}{2}\) thì |2x - 1| = 2x - 1; |2x + 3| = 2x + 3

Ta có: 2.|2x - 1| - 3.|2x + 3| = 2.(2x - 1) - 3.(2x + 3)

= 4x - 2 - 6x - 9

= -2x - 11

Đúng thì thôi c` sai thì cấm chửi

ta có :

+)\(\frac{a}{a-b}\)= \(\frac{a}{a}\)- \(\frac{a}{b}\)= 1-\(\frac{a}{b}\)

+) \(\frac{c}{c-d}\)= \(\frac{c}{c}\)-\(\frac{c}{d}\)= 1 -\(\frac{c}{d}\)

mà \(\frac{a}{b}\)= \(\frac{c}{d}\)=> \(\frac{a}{a-b}\)=\(\frac{c}{c-d}\)

\(\frac{a}{b}=\frac{c}{d}\Leftrightarrow ad=bc\)

\(\Rightarrow ac-ad=ac-bc\) 

\(\Rightarrow a\left(c-d\right)=c\left(a-b\right)\)

\(\Rightarrow\frac{a}{a-b}=\frac{c}{c-d}\)

\(\frac{x-18}{x+4}=\frac{x-17}{x+16}\Leftrightarrow\left(x-18\right)\left(x+16\right)=\left(x-17\right)\left(x+4\right)\)
\(\Leftrightarrow x^2+16x-18x-18\cdot16=x^2+4x-17x-17\cdot4\)
\(\Leftrightarrow-2x-288=-13x-68\Leftrightarrow-2x+13x=-68+288\)
\(\Leftrightarrow11x=220\Leftrightarrow x=\frac{220}{11}=20\)