Zerlegen in lineare Faktoren: Term mit Brüchen \(x^2+\frac{8}{15}x +\frac{1}{15}\)
\(x^2+\frac{8}{15}x +\frac{1}{15}=0|-\frac{1}{15}\)
\(x^2+\frac{8}{15}x=-\frac{1}{15}\) quadratische Ergänzung
\(x^2+\frac{8}{15}x+(\frac{4}{15})^2=-\frac{1}{15}+(\frac{4}{15})^2\) 1.Binom
\((x+\frac{4}{15})^2=-\frac{15}{225}+\frac{16}{225}=\frac{1}{225}|±\sqrt{~~}\)
1.)
\(x+\frac{4}{15}=\frac{1}{15}\)
\(x_1=-\frac{1}{5}\)
2.)
\(x+\frac{4}{15}=-\frac{1}{15}\)
\(x_2=-\frac{1}{3}\)
\(x^2+\frac{8}{15}x +\frac{1}{15}=(x+\frac{1}{5})(x+\frac{1}{3})\)
