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

Lösung

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

x = \frac{b ( a - b )}{b + a}; b (a - b) (b + a) \neq = 0, b \neq = - a

Schritte zur Lösung

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

Multipliziere mit dem kleinsten gemeinsamen Multiplikator

x (a - b) (b + a) + b x (b + a) = ba (a - b); b (a - b) (b + a) \neq = 0

Multipliziere aus

x (a - b) (b + a) : a^{2} x - b^{2} x

a^{2} x - b^{2} x + b x (b + a) = ba (a - b)

Multipliziere aus

b x (b + a) : b^{2} x + ba x

a^{2} x - b^{2} x + b^{2} x + ba x = ba (a - b)

Addiere gleiche Elemente:

- b^{2} x + b^{2} x = 0

a^{2} x + ba x = ba (a - b)

Schreibe

ba (a - b)

um:

b a^{2} - b^{2} a

a^{2} x + ba x = b a^{2} - b^{2} a; b (a - b) (b + a) \neq = 0

Faktorisiere

a^{2} x + ba x : a x (a + b)

a x (a + b) = b a^{2} - b^{2} a; b (a - b) (b + a) \neq = 0

Teile beide Seiten durch

a (a + b); b (a - b) (b + a) \neq = 0, b \neq = - a

x = \frac{b ( a - b )}{b + a}; b (a - b) (b + a) \neq = 0, b \neq = - a

so l v e f or x, 4 x - 6 y = 9

so l v e f or x, x - 3 y - 5 = 12

11 + \frac{6 - x}{2} = 26

5 n + 5 = 20 (4 + 0.25 n)

so l v e f or r, r (x) = \frac{x ^{2} - 9}{x + b}