vereinfachen (1-1/((x+28)^2))(1-1/((x+29)^2))

Lösung

vereinfachen

(1 - \frac{1}{( x + 28 ) ^{2}}) (1 - \frac{1}{( x + 29 ) ^{2}})

\frac{( x + 27 ) ( x + 30 )}{( x + 29 ) ( x + 28 )}

Schritte zur Lösung

(1 - \frac{1}{( x + 28 ) ^{2}}) (1 - \frac{1}{( x + 29 ) ^{2}})

Füge zusammen:

1 - \frac{1}{( x + 28 ) ^{2}} : \frac{x ^{2} + 56 x + 783}{( x + 28 ) ^{2}}

= \frac{x ^{2} + 56 x + 783}{( x + 28 ) ^{2}} (1 - \frac{1}{( x + 29 ) ^{2}})

Wende Bruchregel an:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( x ^{2} + 56 x + 783 ) ( 1 - \frac{1}{( x + 29 ) ^{2}} )}{( x + 28 ) ^{2}}

Vereinfache

(x^{2} + 56 x + 783) (1 - \frac{1}{( x + 29 ) ^{2}}) : \frac{( x + 27 ) ( x ^{2} + 58 x + 840 )}{x + 29}

= \frac{\frac{( x + 27 ) ( x ^{2} + 58 x + 840 )}{x + 29}}{( x + 28 ) ^{2}}

Wende Bruchregel an:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( x + 27 ) ( x ^{2} + 58 x + 840 )}{( x + 29 ) ( x + 28 ) ^{2}}

Faktorisiere

x^{2} + 58 x + 840 : (x + 28) (x + 30)

= \frac{( x + 27 ) ( x + 28 ) ( x + 30 )}{( x + 29 ) ( x + 28 ) ^{2}}

Wende Exponentenregel an:

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

(x + 28)^{2} = (x + 28) (x + 28)

= \frac{( x + 27 ) ( x + 28 ) ( x + 30 )}{( x + 29 ) ( x + 28 ) ( x + 28 )}

Streiche die gemeinsamen Faktoren:

x + 28

= \frac{( x + 27 ) ( x + 30 )}{( x + 29 ) ( x + 28 )}

e x p an d 4 x^{2} (3 x^{3} + 1 - x)

e x p an d - 2 (π \cdot (x + 1)^{3}) + 37

e x p an d 2 (\frac{2 ( - 1 ) ^{n} - 2}{π ^{3} n ^{3}} - \frac{2 ( - 1 ) ^{n}}{πn})

e x p an d (y + 4) - sin^{2} (2 y) + cos^{2} (2 x)

e x p an d \frac{[ x - 1 ]}{[ ( x + 1 ) ( x - 5 ) ( x + 7 ) ]}