vereinfachen (4a^2-20a+25)/(25-4a^2)

Lösung

vereinfachen

\frac{4 a ^{2} - 20 a + 25}{25 - 4 a ^{2}}

- \frac{2 a - 5}{5 + 2 a}

Schritte zur Lösung

\frac{4 a ^{2} - 20 a + 25}{25 - 4 a ^{2}}

Faktorisiere

4 a^{2} - 20 a + 25 : (2 a - 5)^{2}

= \frac{( 2 a - 5 ) ^{2}}{25 - 4 a ^{2}}

Faktorisiere

25 - 4 a^{2} : (5 + 2 a) (5 - 2 a)

= \frac{( 2 a - 5 ) ^{2}}{( 5 + 2 a ) ( 5 - 2 a )}

(5 + 2 a) (5 - 2 a) = - (5 + 2 a) (2 a - 5)

= \frac{( 2 a - 5 ) ^{2}}{- ( 5 + 2 a ) ( 2 a - 5 )}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(2 a - 5)^{2} = (2 a - 5) (2 a - 5)

= \frac{( 2 a - 5 ) ( 2 a - 5 )}{- ( 5 + 2 a ) ( 2 a - 5 )}

Streiche die gemeinsamen Faktoren:

2 a - 5

= \frac{2 a - 5}{- ( 5 + 2 a )}

Wende Bruchregel an:

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

= - \frac{2 a - 5}{5 + 2 a}

l o n g d i v i s i o n \frac{14}{4}

f a c t or x^{2} + 2 x y - 8 y^{2}

m^{2} + 8 m - 81 = 0

(7 x - 2)^{2} = 16

2 z + 4 \geq - 4