Aufgabe:
Partialbruchzerlegung der Funktion
y = (x^4+7x^3-36x^2-203x+397)÷(x^3+12x^2+21x-98)
Text erkannt:
Partialbrecndeleging
\( y=\frac{x^{4}+7 x^{3}-36 x^{2}-203 x+397}{x^{3}+12 x^{2}+21 x-98}=\frac{P(x)}{Q x x y} \quad m>n \) unecht ghrochen
\( \left(x^{3}+12 x^{2}+21 x-98\right):(y-2)=x^{2}+14 x+49 \) lpq-tormel \( x_{11}=-\frac{\text { f }}{2-} \sqrt{\left(\frac{1}{2}\right)^{2}-q^{3}} \)
\( -\left(x^{3}-2 x^{2}\right) \)
\( \begin{aligned} \frac{-\left(x^{3}-2 x^{2}\right)}{14 x^{2}+21 x} & x_{213}=-\frac{14}{2} \pm \sqrt{\left(\frac{14}{2}\right)^{2}} \\ \frac{-\left(14 x^{2}-28 x\right)}{49 x-98} & x_{2,3}=-7 \pm 0 \\ \frac{-(49 x-98)}{0} & x_{2,3}=-7 \end{aligned} \)
\( \begin{array}{l} \frac{P(x)}{Q(x)}=\frac{A}{(x-2)}+\frac{B}{(x+7)}+\frac{C}{(x+7)} \\ \frac{P(x)}{Q(x)}=\frac{A(x-2) \cdot(x+7) \cdot(x+7)}{(x)}+\frac{B(x+7) \cdot(x-2) \cdot(x+7)}{(x+7)}+\frac{C-(x+7) \cdot(x-2) \cdot(x+7)}{(x+7)} \\ P(x)=A(x+7) \cdot(x+7)+B(x-2) \cdot(x+7)+((x-2) \cdot(x+7) \\ 3 x^{2}-93=A(x+7)^{2}+B(x-2) \cdot(x+7)+((x-2) \cdot(x+7) \end{array} \)
\( \begin{array}{l} x_{1}=2 \quad \Rightarrow \quad-81=81 A \Leftrightarrow A=-1 \\ x_{2}=-7 \quad \Rightarrow \quad 54=0 \\ x_{3}=-7 \quad \Rightarrow \quad 54=0 \end{array} \)
\( f(x)=x-5-\frac{1}{(x-2)} \)
Problem/Ansatz:
Falsches Ergebnis
