((x+1)^2+14)/(4x+5)=n

Lösung

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} = n

x = - 1 + 2 n + 4 n^{2} + n - 14, x = - 1 + 2 n - 4 n^{2} + n - 14

Schritte zur Lösung

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} = n

Vereinfache

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} : \frac{x ^{2} + 2 x + 15}{4 x + 5}

\frac{x ^{2} + 2 x + 15}{4 x + 5} = n

Multipliziere beide Seiten mit

4 x + 5

x^{2} + 2 x + 15 = n (4 x + 5)

Löse

x^{2} + 2 x + 15 = n (4 x + 5) : x = - 1 + 2 n + 4 n^{2} + n - 14, x = - 1 + 2 n - 4 n^{2} + n - 14

x = - 1 + 2 n + 4 n^{2} + n - 14, x = - 1 + 2 n - 4 n^{2} + n - 14

\frac{1}{x ^{2}} - \frac{5}{x} + 2 = 0

\frac{5}{( 2 x ^{2} )} - \frac{1}{( 6 x ^{2} )} = \frac{7}{12}

0 = \frac{2}{3 x + 2}

\frac{1}{2 \cdot ( x + \frac{1}{5} )} = \frac{9}{5}

\frac{2}{( 5 x )} - \frac{1}{30} = \frac{5}{( 2 x )}