\(\frac{-5}{9}x+1=\frac{2}{3}x-10\)

\(\frac{-5}{9}x+\frac{9}{9}=\frac{6}{9}x-\frac{90}{9}\)

\(-5x+9=6x-90\)

\(-5x-6x=-90-9\)

\(-11x=-99\)

\(x=\frac{-99}{-11}=9\)

b. \(\frac{x-22}{8}+\frac{x-21}{9}+\frac{x-20}{10}+\frac{x-19}{11}=4\)

\(\frac{x-22}{8}-1+\frac{x-21}{9}-1+\frac{x-20}{10}-1+\frac{x-19}{11}-1=0\)

\(\frac{x-30}{8}+\frac{x-30}{9}+\frac{x-30}{10}+\frac{x-30}{11}=0\)

\(\left(x-30\right)\left(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)=0\)

x=30

Chúc bạn học tốt!!

a) \(\frac{15x-10}{x^2+3}=0\)

<=> 15x - 10 = 0

<=> 5(3x - 2) = 0

<=> 3x - 2 = 0

<=> 3x = 2

<=> x = 2/3

b) ĐKXĐ: \(x\ne1;x\ne-3\)

<=>\(\frac{3x-1}{x-1}-\frac{2x+5}{x+3}-\frac{8}{x^2+2x-3}=0\)

<=> \(\frac{3x-1}{x-1}-\frac{2x+5}{x+3}-\frac{8}{\left(x-1\right)\left(x+3\right)}=0\)

<=> (3x - 1)(x + 3) - (2x + 5)(x - 1) - 8 = (x - 1)(x + 3)

<=> 3x² + 9x - x - 3 - 2x² + 2x - 5x + 5 - 8 = 0

<=> x² + 5x - 6 = 0

<=> (x - 1)(x + 6) = 0

<=> x - 1 = 0 hoặc x + 6 = 0

<=> x = 1 (ktm) hoặc x = -6 (tm)

=> x = -6

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

\(\Leftrightarrow x^2-2\cdot x\cdot\frac{1}{x}+\frac{1}{x^2}+x-\frac{1}{x}=0\)

\(\Leftrightarrow\left(x-\frac{1}{x}\right)^2+\left(x-\frac{1}{x}\right)=0\)

\(\Leftrightarrow\left(x-\frac{1}{x}\right)\left(x-\frac{1}{x}+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{x}=0\\x-\frac{1}{x}+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\frac{x^2-1}{x}=0\\\frac{x^2+x-1}{x}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2-1=0\\x^2+x-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)\left(x+1\right)=0\\x^2+2\cdot x\cdot\frac{1}{2}+\frac{1}{4}-\frac{5}{4}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\pm1\\\left(x+\frac{1}{2}\right)^2=\frac{5}{4}=\left(\frac{\pm\sqrt{5}}{2}\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\pm1\\x=\frac{\pm\sqrt{5}-1}{2}\end{matrix}\right.\)

Vậy....

ĐKXĐ: x ≠ \(\pm\) 1

Từ phương trình ban đầu suy ra:

\(x^2\left(x+1\right)^2+x^2\left(x-1\right)^2=\frac{10}{9}.\left(x^2-1\right)^2\)

⇒ \(x^4+2x^3+x^2+x^4-2x^3+x^2=\frac{10}{9}\left(x^4-2x^2+1\right)\)

⇒ \(18\left(x^4+x^2\right)=10\left(x^4-2x^2+1\right)\)

⇒ \(4x^4+19x^2-5=0\Leftrightarrow\left(x^2+5\right)\left(4x^2-1\right)=0\)

⇔ \(x^2=\frac{1}{4}\Leftrightarrow x=\pm\frac{1}{2}\)( thỏa mãn ĐKXĐ)

Vậy ...

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

\(\Leftrightarrow\left(x^2-2+\frac{1}{x^2}\right)-2\left(x-\frac{1}{x}\right)+1=0\)

\(\Leftrightarrow\left(x-\frac{1}{x}\right)^2-2\left(x-\frac{1}{x}\right)+1=0\)

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

\(\Leftrightarrow x-\frac{1}{x}-1=0\)

Làm nôt