erweitern (((Ax)-1)^2)/(((Bx)-1)^2((Cx)-1)^2)

Lösung

erweitern

\frac{( ( A \cdot x ) - 1 ) ^{2}}{( ( B \cdot x ) - 1 ) ^{2} \cdot ( ( C \cdot x ) - 1 ) ^{2}}

\frac{A ^{2} x ^{2} - 2 A x + 1}{B ^{2} C ^{2} x ^{4} - 2 B ^{2} C x ^{3} + B ^{2} x ^{2} - 2 B C ^{2} x ^{3} + 4 BC x ^{2} - 2 B x + C ^{2} x ^{2} - 2 C x + 1}

Schritte zur Lösung

\frac{( ( A x ) - 1 ) ^{2}}{( ( B x ) - 1 ) ^{2} ( ( C x ) - 1 ) ^{2}}

Entferne die Klammern:

(a) = a

= \frac{( A x - 1 ) ^{2}}{( B x - 1 ) ^{2} ( C x - 1 ) ^{2}}

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

= \frac{( A x - 1 ) ^{2}}{( B ^{2} x ^{2} - 2 B x + 1 ) ( C x - 1 ) ^{2}}

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

= \frac{( A x - 1 ) ^{2}}{( B ^{2} x ^{2} - 2 B x + 1 ) ( C ^{2} x ^{2} - 2 C x + 1 )}

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

= \frac{A ^{2} x ^{2} - 2 A x + 1}{( B ^{2} x ^{2} - 2 B x + 1 ) ( C ^{2} x ^{2} - 2 C x + 1 )}

Multipliziere aus

(B^{2} x^{2} - 2 B x + 1) (C^{2} x^{2} - 2 C x + 1) : B^{2} C^{2} x^{4} - 2 B^{2} C x^{3} + B^{2} x^{2} - 2 B C^{2} x^{3} + 4 BC x^{2} - 2 B x + C^{2} x^{2} - 2 C x + 1

= \frac{A ^{2} x ^{2} - 2 A x + 1}{B ^{2} C ^{2} x ^{4} - 2 B ^{2} C x ^{3} + B ^{2} x ^{2} - 2 B C ^{2} x ^{3} + 4 BC x ^{2} - 2 B x + C ^{2} x ^{2} - 2 C x + 1}

e x p an d \frac{tan ( t )}{( t - 3 ) ( t - 5 )}

s im pl i f y (x - 2) (x + \frac{3}{4})

s im pl i f y (3 x - 4) (2 x - 1)

e x p an d e^{x} (\frac{d y}{d x} + y)

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