erweitern (sqrt(2)-sqrt(x-3))(sqrt(x-1)+2)

Lösung

erweitern

(2 - x - 3) (x - 1 + 2)

2 x - 1 + 22 - x^{2} - 4 x + 3 - 2 x - 3

Schritte zur Lösung

(2 - x - 3) (x - 1 + 2)

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = 2, b = - x - 3, c = x - 1, d = 2

= 2 x - 1 + 2 \cdot 2 + (- x - 3) x - 1 + (- x - 3) \cdot 2

Wende Minus-Plus Regeln an

+ (- a) = - a

= 2 x - 1 + 22 - x - 3 x - 1 - 2 x - 3

x - 3 x - 1 = x^{2} - 4 x + 3

= 2 x - 1 + 22 - x^{2} - 4 x + 3 - 2 x - 3

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

e x p an d c u r l (x^{2} y, yz, x - z)

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

e x p an d \frac{3 x}{2} - \frac{3}{2 π} (100 - 3 x)

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