erweitern (4x^3-21x^2-10x+25)/(x^2(x-5)^2)

Lösung

erweitern

\frac{4 x ^{3} - 21 x ^{2} - 10 x + 25}{x ^{2} ( x - 5 ) ^{2}}

\frac{4 x ^{3} - 21 x ^{2} - 10 x + 25}{x ^{4} - 10 x ^{3} + 25 x ^{2}}

Schritte zur Lösung

\frac{4 x ^{3} - 21 x ^{2} - 10 x + 25}{x ^{2} ( x - 5 ) ^{2}}

(x - 5)^{2} = x^{2} - 10 x + 25

= \frac{4 x ^{3} - 21 x ^{2} - 10 x + 25}{x ^{2} ( x ^{2} - 10 x + 25 )}

Multipliziere aus

x^{2} (x^{2} - 10 x + 25) : x^{4} - 10 x^{3} + 25 x^{2}

= \frac{4 x ^{3} - 21 x ^{2} - 10 x + 25}{x ^{4} - 10 x ^{3} + 25 x ^{2}}

e x p an d \frac{1}{( x - 5 ) ^{2}}

s im pl i f y (5 x - 2) (5 x + 2)

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + y^{2} - 25))

e x p an d (tan (x) + sec (x)) (1 - sin (x))

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