erweitern ((x-1)^{1/2}(x+3)^2)/(x+3^{1/2)}

Lösung

erweitern

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

\frac{x ^{2} ( x - 1 ) ^{\frac{1}{2}} + 6 x ( x - 1 ) ^{\frac{1}{2}} + 9 ( x - 1 ) ^{\frac{1}{2}}}{x + 3 ^{\frac{1}{2}}}

Schritte zur Lösung

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

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

= \frac{( x ^{2} + 6 x + 9 ) ( x - 1 ) ^{\frac{1}{2}}}{x + 3 ^{\frac{1}{2}}}

Multipliziere aus

(x - 1)^{\frac{1}{2}} (x^{2} + 6 x + 9) : x^{2} (x - 1)^{\frac{1}{2}} + 6 x (x - 1)^{\frac{1}{2}} + 9 (x - 1)^{\frac{1}{2}}

= \frac{x ^{2} ( x - 1 ) ^{\frac{1}{2}} + 6 x ( x - 1 ) ^{\frac{1}{2}} + 9 ( x - 1 ) ^{\frac{1}{2}}}{x + 3 ^{\frac{1}{2}}}

e x p an d \frac{x - 9}{x ( x - 3 )}

e x p an d - 3 (a + 5) (a + 3)^{'}

e x p an d sin (3 u) sin (3 (t - u))

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

e x p an d \frac{1}{x ^{2}} (x^{2} + y^{2} = 9) (\frac{1}{y ^{2}})