a/(ax-1)+b/(bx-1)=a+b

Lösung

\frac{a}{a x - 1} + \frac{b}{b x - 1} = a + b

x = \frac{a + b}{ab}, x = \frac{2}{b + a}; a b^{2} + a^{2} b \neq = 0

Schritte zur Lösung

\frac{a}{a x - 1} + \frac{b}{b x - 1} = a + b

Multipliziere mit dem kleinsten gemeinsamen Multiplikator

a (b x - 1) + b (a x - 1) = a (a x - 1) (b x - 1) + b (a x - 1) (b x - 1)

Löse

a (b x - 1) + b (a x - 1) = a (a x - 1) (b x - 1) + b (a x - 1) (b x - 1) : x = \frac{a + b}{ab}, x = \frac{2}{b + a}; a b^{2} + a^{2} b \neq = 0

x = \frac{a + b}{ab}, x = \frac{2}{b + a}; a b^{2} + a^{2} b \neq = 0

\frac{x ^{2} + 4}{x - 1} = \frac{5}{x - 1}

9 + \frac{x}{x - 1} = \frac{1}{x ^{2} - x}

\frac{20}{x} = x + 1

\frac{10}{x + 6} = 1

\frac{x + 2}{x + 3} + \frac{3}{x ^{2} + 6 x + 9} = 1