"\\frac{6x-1}{(x-3)(x+1)}=\\frac{A}{x-3}+\\frac{B}{x+1}=\\frac{A(x+1)+B(x-3)}{(x-3)(x+1)}=\\frac{Ax+A+Bx-3B}{(x-3)(x+1)}=\\frac{x(A+B)+A-3B}{(x-3)(x+1)}"
"\\begin{cases}\n A+B=6 \\\\\nA-3B=-1\n\\end{cases}"
"\\begin{cases}\n A+B=6 \\\\\nA=3B-1\n\\end{cases}"
"3B-1+B=6"
"4B=7"
"B=\\frac{7}{4}"
"A=3\\cdot\\frac{7}{4}-1=\\frac{17}{4}"
"\\frac{6x-1}{(x-3)(x+1)}=\\frac{17}{4(x-3)}+\\frac{7}{4(x+1)}"
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