\(x-\frac{6}{7}+x-\frac{7}{8}+x-\frac{8}{9}=x-\frac{9}{10}+x-\frac{10}{11}+x-\frac{11}{12}\)

\(x+x+x-x-x-x=\frac{6}{7}+\frac{7}{8}+\frac{8}{9}-\frac{9}{10}-\frac{10}{11}-\frac{11}{12}\)

\(0=\frac{6}{7}+\frac{7}{8}+\frac{8}{9}-\frac{9}{10}-\frac{10}{11}-\frac{11}{12}\)

X triệt tiêu hết ròi! Vậy đề bài yêu cầu tìm gì vậy. Nhưng mà...giá trị của 2 vế ko bằng nhau.

\(\Leftrightarrow\left(\frac{x+1}{7}-1\right)+\left(\frac{x+1}{8}-1\right)+\left(\frac{x+1}{9}-1\right)=\left(\frac{x+1}{10}-1\right)+\left(\frac{x+1}{11}-1\right)+\left(\frac{x+1}{12}-1\right)\)

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)=0\)

\(\text{Vì}\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\ne\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\)\(\Rightarrow\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\ne0\)

\(\Rightarrow x+1=0\)

\(\Rightarrow x=-1\)

\(\Leftrightarrow\frac{x-6}{7}+1+\frac{x-7}{8}+1+\frac{x-8}{9}+1=\frac{x-9}{10}+1+\frac{x-10}{11}+1\)\(+\frac{x-11}{12}+1\) ( cộng 2 vế với 3 )

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)=0\)

\(\Leftrightarrow x+1=0\) \(\left(do\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\right)\)

\(\Leftrightarrow x=-1\)

|x-10| = x+6

Phân số tối giản là `5/9`

\(x-\dfrac{1}{4}=\dfrac{5}{3}:\dfrac{2}{3}\)

\(x-\dfrac{1}{4}=\dfrac{5}{3}\times\dfrac{3}{2}\)

\(x-\dfrac{1}{4}=\dfrac{5}{2}\)

\(x=\dfrac{5}{2}+\dfrac{1}{4}\)

\(x=\dfrac{11}{4}\)

phân ssoos tối giản là 5/9

x - 1/4 = 5/3 : 2/3

x - 1/4 = .5/3 x 3/2

x - 1/4 = 5/2

x         = .5/2 + 1/4

x         =.11/4

\(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}\)và \(5x+y-2z=28\)

1. Tìm x, biết:

a) \(\frac{4}{x}=\frac{8}{6}\). Ta có: \(\frac{8}{6}=\frac{8:2}{6:2}=\frac{4}{3}\Rightarrow x=3\)

b) \(\frac{3}{x-5}=\frac{4}{x+2}\). Ta có: \(5-2=3\)

\(\Rightarrow x=\left(3.5\right)+\left(4.2\right)+3=15+8+3=26\)

c) \(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x=\left(-8\right):\left(-2\right)=4\)

2. Rút gọn

a) \(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}\Leftrightarrow\frac{2^3.2^1.5^2.11.11.7}{2^3.5^2.5^1.7.7.11}\Leftrightarrow\frac{2^1.11}{5^1.7}=\frac{22}{35}\)

b) Tương tự

c) Tương tự

\(\frac{4}{x}=\frac{8}{6}\Rightarrow x=\frac{4.6}{8}=3\)

\(\frac{3}{x-5}=\frac{-4}{x+2}\Rightarrow3\left(x+2\right)=-4\left(x-5\right)\)

                                \(\Rightarrow3x+6=-4x+20\)

                                \(\Rightarrow3x+4x=20-6\)

                                \(\Rightarrow7x=14\)

                                \(\Rightarrow x=2\)

\(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x^2=\left(-8\right)\left(-2\right)=16\Rightarrow x=\pm4\)

\(\frac{4}{x}=\frac{8}{6}\)

\(\Rightarrow4\cdot6=x\cdot8\)

\(\Rightarrow x=\frac{4\cdot6}{8}\)

\(\Rightarrow x=3\)

x=-1               

x=-1                                 

x = -1

ai tk mk

mk tk lại

hứa luôn

thank nhiều

Công mỗi phân số cho 1 .....................

 mỗi hạng tử ở 2 vế cộng với 1 (có nghĩa là cộng 2 vế với 3 xong chia đều ra 3 hạng tử mỗi hạng tử cộng với 1)

Sau đó sẽ dẫn đến tất cả các hạng tử đều có chung tử số rồi nhóm tử ra ngoài là được 

\(\frac{x-6}{7}+\frac{x-7}{8}+\frac{x-8}{9}=\frac{x-9}{10}+\frac{x-10}{11}+\frac{x-11}{12}\)

Cộng mỗi p/s cho 1,ta đc:

\(\frac{x-6}{7}+1+\frac{x-7}{8}+1+\frac{x-8}{9}+1=\frac{x-9}{10}+1+\frac{x-10}{11}+1+\frac{x-11}{12}+1\)

\(\Leftrightarrow\frac{x-6+7}{7}+\frac{x-7+8}{8}+\frac{x-8+9}{9}=\frac{x-9+10}{10}+\frac{x-10+11}{11}+\frac{x-11+12}{12}\)

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\left(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\right)=0\)

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}-\frac{x+1}{11}-\frac{x+1}{12}=0\)

\(\Leftrightarrow\left(x+1\right).\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)=0\)

Vì \(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\)

=>x+1=0

=>x=-1

\(\dfrac{10.4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{5.2.2^{12}.3^{10}+3^9.2^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{5.2^{13}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}=\dfrac{2^{12}.3^{10}.5\left(2+1\right)}{2^{11}.3^{11}.5}\)

\(=\dfrac{2^{11}.2.3^{10}.5.3}{2^{11}.3^{10}.3.5}=2\)