\(x^2-x-\frac{3}{4}=0\)

\(\Rightarrow\frac{x^2-x}{1}-\frac{3}{4}=0\)

\(\Rightarrow\frac{\left(x^2-x\right).4}{4}-\frac{3}{4}=0\)

\(\Rightarrow\frac{4x^2-4x-3}{4}=0\)

\(\Rightarrow4x^2-4x-3=0\)

\(\Rightarrow4x^2-6x+2x-3=0\)

\(\Rightarrow2x\left(2x-3\right)+\left(2x-3\right)=0\)

\(\Rightarrow\left(2x+1\right)\left(2x-3\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x+1=0\\2x-3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{3}{2}\end{cases}}}\)

\(x^2-x-\frac{3}{4}=0\)

<=>  \(x^2-x+\frac{1}{4}-1=0\)

<=>  \(\left(x-\frac{1}{2}\right)^2-1=0\)

<=>  \(\left(x-\frac{1}{2}-1\right)\left(x-\frac{1}{2}+1\right)=0\)

<=> \(\left(x-\frac{3}{2}\right)\left(x+\frac{1}{2}\right)=0\)

làm nốt nhé

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

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

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

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

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

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

\(\Leftrightarrow x=-1\)

Vậy x=-1

mỗi phân số + 1 thì sẽ có tử chung là x + 1

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

mà tổng các phân số kia khác 0 nên x+1 bằng 0 

=> x=-1

\(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\)và x + y -z = 10 

\(\frac{x}{2}=\frac{y}{3}=\frac{1}{4}.\frac{x}{2}=\frac{1}{4}.\frac{y}{3}\)\(=\frac{x}{8}=\frac{y}{12}\)

\(\frac{y}{4}=\frac{z}{5}=\frac{1}{3}.\frac{y}{4}=\frac{1}{3}.\frac{z}{5}=\frac{y}{12}=\frac{z}{15}\)

\(\Leftrightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)và x + y - z = 10 

Theo tính chất dãy tỉ số bằng nhau: 

\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)

* \(\frac{x}{8}=2\Rightarrow x=2.8=16\)

*  \(\frac{y}{12}=2\Rightarrow y=2.12=24\)

* \(\frac{z}{5}=2\Rightarrow z=2.5=10\)

Vậy...

Ý mk nhầm chút xíu nhé! Cko sorry! 

* \(\frac{z}{15}=2\Rightarrow z=2.15=30\)

... :( Xl

\(\Leftrightarrow\frac{x-2012}{2}-1+\frac{x-2008}{3}-2+\frac{x-2002}{4}-3+\frac{x-1994}{5}-4=0\)

\(\Leftrightarrow\frac{x-2014}{2}+\frac{x-2014}{3}+\frac{x-2014}{4}+\frac{x-2014}{5}=0\)

\(\Leftrightarrow\left(x-2014\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)=0\)

\(\Leftrightarrow x-2014=0\)

\(\Leftrightarrow x=2014\)

Bài 1:

a)  \(x-\frac{20}{11.13}-\frac{20}{13.15}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)

\(x-\frac{20}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10\cdot\frac{4}{55}=\frac{3}{11}\)

\(x-\frac{8}{11}=\frac{3}{11}\)

\(x=1\)

b) \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(2.\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(2.\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

=> x + 1 =18

x = 17

bài 2 ko bk lm, xl nha

mk cảm ơn bn nha

không bít

     \(x^2-x-\frac{3}{4}=0\)

\(\Rightarrow x^2+\frac{1}{2}x-\frac{3}{2}x-\frac{3}{4}=0\)

\(\Rightarrow x\left(x+\frac{1}{2}\right)-\frac{3}{2}\left(x+\frac{1}{2}\right)=0\)

\(\Rightarrow\left(x-\frac{3}{2}\right)\left(x+\frac{1}{2}\right)=0\)

\(\Rightarrow\hept{\begin{cases}x-\frac{3}{2}=0\\x+\frac{1}{2}=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{3}{2}\\x=-\frac{1}{2}\end{cases}}}\)

Chúc bạn học tốt.

Đề bài thiếu nha bạn

nhưng mà mình chỉ biết thế thôi thiếu gì thì bổ sung, còn làm dc thì làm luôn nha đung mình k