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\(a)=\frac{-2\left(x+3\right)}{x\left(1-3x\right)}.\frac{1-3x}{x\left(x+3\right)}\)
\(=\frac{-2}{x^2}\)
\(b)=\frac{\left(x+3\right)\left(x-3\right)}{x\left(x-3\right)}-\frac{x^2}{x\left(x-3\right)}+\frac{9}{x\left(x-3\right)}\)
\(=\frac{x^2-3x+3x-9-x^2+9}{x\left(x-3\right)}\)
\(=x\left(x-3\right)\)
\(c)=\frac{x+3}{\left(x-1\right)\left(x+1\right)}-\frac{1}{x\left(x+1\right)}\)
\(=\frac{\left(x+3\right).x}{x\left(x-1\right)\left(x+1\right)}-\frac{1.\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x^2+3x-x+1}{x\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x\left(x+3\right)-\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+3}{x+1}\)
# Sắp ik ngủ nên làm vậy hoi, ko chắc phần kq câu b và c đâu nha
\(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^2}\)
\(=\frac{3x+2}{9x^2-4}-\frac{3x-2}{9x^2-4}+\frac{3x-6}{9x^2-4}\)
\(=\frac{3x+2-3x+2+3x-6}{9x^2-4}\)
\(=\frac{3x-2}{9x^2-4}\)
\(=\frac{1}{3x+2}\)
\(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x^2}{x^2-9}\)
\(=\frac{18}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\) \(-\frac{3\left(x+3\right)}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)\(-\frac{x^2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x-3\right)}\)
\(=\frac{18-3x-9-x^3+3x^2}{\left(x-3\right)^2\left(x+3\right)}\)
\(=\frac{-x^3+3x^2-3x+9}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{\left(-x^2-3\right)\left(x-3\right)}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{-x^2-3}{\left(x-3\right)\left(x+3\right)}\)
học tốt
ĐKXĐ : \(\hept{\begin{cases}x-2\ne0\\3-4x\ne0\end{cases}\Rightarrow\hept{\begin{cases}x\ne2\\x\ne\frac{3}{4}\end{cases}}}\)
\(\frac{5}{x-2}+\frac{6}{3-4x}=0\)
\(\frac{5\left(3-4x\right)}{\left(x-2\right)\left(3-4x\right)}+\frac{6\left(x-2\right)}{\left(3-4x\right)\left(x-2\right)}=0\)
\(15-20x+6x-12=0\)
\(3-14x=0\Leftrightarrow14x=3\Leftrightarrow x=\frac{3}{14}\)theo ĐKXĐ : x thỏa mãn
\(a,\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^2}\)
\(=\frac{1}{3x-2}-\frac{1}{3x+2}+\frac{3\left(x-2\right)}{\left(3x+2\right)\left(3x-2\right)}\)
\(=\frac{3x+2-\left(3x-2\right)+3\left(x-2\right)}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\frac{3x+2-3x+2+3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\frac{3x-2}{\left(3x-2\right)\left(3x+2\right)}=\frac{1}{3x+2}\)
\(b,\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x}{x^2-9}\)
\(=\frac{18}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}-\frac{3}{\left(x-3\right)\left(x-3\right)}-\frac{x}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{18-3\left(x+3\right)-x\left(x-3\right)}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)
\(=\frac{18-3x-9-x^2+3x}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)
\(=\frac{-x^2+9}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)
\(=\frac{-\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}=-\frac{1}{x-3}\)