erweitern ((x-4)(x-5))/((x-3)^2(x+1)^2)

Lösung

erweitern

\frac{( x - 4 ) ( x - 5 )}{( x - 3 ) ^{2} ( x + 1 ) ^{2}}

\frac{x ^{2} - 9 x + 20}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}

Schritte zur Lösung

\frac{( x - 4 ) ( x - 5 )}{( x - 3 ) ^{2} ( x + 1 ) ^{2}}

(x - 3)^{2} = x^{2} - 6 x + 9

= \frac{( x - 4 ) ( x - 5 )}{( x ^{2} - 6 x + 9 ) ( x + 1 ) ^{2}}

(x + 1)^{2} = x^{2} + 2 x + 1

= \frac{( x - 4 ) ( x - 5 )}{( x ^{2} - 6 x + 9 ) ( x ^{2} + 2 x + 1 )}

Multipliziere aus

(x^{2} - 6 x + 9) (x^{2} + 2 x + 1) : x^{4} - 4 x^{3} - 2 x^{2} + 12 x + 9

= \frac{( x - 4 ) ( x - 5 )}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}

Multipliziere aus

(x - 4) (x - 5) : x^{2} - 9 x + 20

= \frac{x ^{2} - 9 x + 20}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}

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

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

e x p an d \frac{( ( 2 x - 1 ) ^{3} ( 26 - 6 x ) )}{( 4 - x ) ^{3}}

e x p an d \frac{d}{d x} ((x - 2) (x - 5)^{3}) + 5

e x p an d (\frac{2 x - 1}{x + 1})^{2}