化简 ((sqrt(x)-x^2)(1+sqrt(x)))/(1-x)

解答

化简

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

\frac{x + x - x ^{2} - x ^{2} x}{1 - x}

求解步骤

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

使用 FOIL 方法:

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

(x - x^{2}) (1 + x) = x \cdot 1 + x x - x^{2} \cdot 1 - x^{2} x

= \frac{x \cdot 1 + x x - x ^{2} \cdot 1 - x ^{2} x}{1 - x}

化简

x \cdot 1 + x x - x^{2} \cdot 1 - x^{2} x : x + x - x^{2} - x^{2} x

= \frac{x + x - x ^{2} - x ^{2} x}{1 - x}

e x p an d (- 9, 7) y (- 9, - 1)

e x p an d \frac{( 5 y + 1 ) ^{2}}{25}

e x p an d (x + 3) l e f t (x - 4)

e x p an d \frac{1}{s ^{2} ( s + 6 )}

e x p an d (- 2 y = (- 1)^{n + 1} + 1) \cdot (- 1)