\(a,\frac{x}{x-3}-\frac{6}{x^2-9}=\frac{1}{x+3}\) (đkxđ: x khác 3, -3)
\(\frac{x\left(x+3\right)-6}{\left(x-3\right)\left(x+3\right)}=\frac{1}{x+3}\)
\(x\left(x+3\right)-6=x-3\)
\(x^2+2x-3=0\)
\(\left(x+3\right)\left(x-1\right)=0\)
\(\Longrightarrow\left[\begin{array}{l}x=-3\left(L\right)\\ x=1\left(N\right)\end{array}\right.\)
\(b,\frac{x^2}{x-2}+\frac{x}{1-x}=\frac{4}{x^2-3x+2}\) (đkxđ: \(x\ne1,x\ne2)\)
\(\frac{x^2}{x-2}-\frac{x}{x-1}=\frac{4}{\left(x-1\right)\left(x-2\right)}\)
\(\frac{x^2\left(x-1\right)-x\left(x-2\right)}{\left(x-1\right)\left(x-2\right)}=\frac{4}{\left(x-1\right)\left(x-2\right)}\)
\(x^2\left(x-1\right)-x\left(x-2\right)=4\)
\(x^3-x^2-x^2+2x=4\)
\(x^3-2x^2+2x-4=0\)
\(\left(x^3-2x^2\right)+\left(2x-4\right)=0\)
\(x^2\left(x-2\right)+2\left(x-2\right)=0\)
\(\left(x-2\right)\left(x^2+2\right)=0\)
vì \(x^2+2>0\forall x\) ⇒ x - 2 = 0
⇒ x = 2 (ko thoả mãn)
vậy phương trình vô nghiệm
