% This file:
%   http://anggtwu.net/LATEX/2024-1-C2-fracoes-parciais-defs.tex.html
%   http://anggtwu.net/LATEX/2024-1-C2-fracoes-parciais-defs.tex
%          (find-angg "LATEX/2024-1-C2-fracoes-parciais-defs.tex")
% Author: Eduardo Ochs <eduardoochs@gmail.com>
%
% (defun e  () (interactive) (find-angg "LATEX/2024-1-C2-fracoes-parciais-defs.tex"))
% (defun oe () (interactive) (find-angg "LATEX/2023-2-C2-edos-exatas-defs.tex"))
% (defun ov () (interactive) (find-angg "LATEX/2023-2-C2-edovs-defs.tex"))

% «.fp-reset»	(to "fp-reset")

\sa   {[FP1]}{\CFname{FP}{_1}}
\sa   {[FP4]}{\CFname{FP}{_4}}
\sa   {[SCD]}{\CFname{S}{_{CD}}}
\def\P#1{\left( #1 \right)}

% «fp-reset»  (to ".fp-reset")
\sa{fp-reset}{
  \sa {A} {A}
  \sa {B} {B}
  \sa {C} {C}
  \sa {D} {D}
  \sa {a} {a}
  \sa {b} {b}
  }
\sa{fp-reset-2}{
  \sa {A} {A}
  \sa {B} {B}
  \sa {C} {(A+B)}
  \sa {D} {(Ab+Ba)}
  \sa {a} {a}
  \sa {b} {b}
  }
\ga{fp-reset}

\sa{(FP1)}{
  \left(\begin{array}{cl}
     & \ga{A}(x+\ga{b}) + \ga{B}(x+\ga{a}) \\\\[-10pt]
    =& \ga{C}x + \ga{D}                    \\
   \end{array}
   \right)
  }

\sa{(FP4)}{
  \left(\begin{array}{rcl}
    \D \frac{\ga{A}}{x+\ga{a}} +
       \frac{\ga{B}}{x+\ga{b}} &=& \D \frac{\ga{A}(x+\ga{b}) +
                                            \ga{B}(x+\ga{a})}
                                           {(x+\ga{a})
                                            (x+\ga{b})}                 \\\\[-10pt]
                               &=& \D \frac{\ga{C}x+\ga{D}}
                                           {(x+\ga{a})
                                            (x+\ga{b})}                 \\\\[-8pt]
    \D \intx{ \frac{\ga{C}x+\ga{D}}
                   {(x+\ga{a})
                    (x+\ga{b})}
            }                  &=& \D \intx { \frac{\ga{A}}{x+\ga{a}} +
                                              \frac{\ga{B}}{x+\ga{b}} } \\\\[-10pt]
                               &=& \ga{A}\ln(x+a) + \ga{B}\ln(x+b)      \\
   \end{array}
   \right)
  }

\sa{(SCD)}{\bmat{C:=(A+B) \\ D:=(Ab+Ba)}}
\sa{(scd)}{\bsm {C:=(A+B) \\ D:=(Ab+Ba)}}






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