化简 sqrt(1+x)(sqrt(1+x)+sqrt(1-x))

解答

化简

1 + x (1 + x + 1 - x)

1 + x + 1 + x 1 - x

求解步骤

1 + x (1 + x + 1 - x)

使用分配律:

a (b + c) = ab + a c

1 + x (1 + x + 1 - x) = 1 + x 1 + x + 1 + x 1 - x

= 1 + x 1 + x + 1 + x 1 - x

使用根式运算法则:

a a = a,

假定

a \geq 0

1 + x 1 + x = 1 + x

= 1 + x + 1 + x 1 - x

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

e x p an d (2 A x + B) e^{x} + e^{x} (A x^{2} + B x + C)

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

e x p an d (\frac{5 x + 4}{x ^{2} - 4}) (\frac{4 x + 2}{x ^{2} - 4})

s im pl i f y (182 - 1) (6)