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受欢迎的代数 >

展开 ((w+1)/(w-1))^2+3((w+1)/(w-1))+K

解答

展开

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

解答

K + \frac{4 w ^{2} + 2 w - 2}{w ^{2} - 2 w + 1}

求解步骤

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

去除括号:

(a) = a

= (\frac{w + 1}{w - 1})^{2} + 3 \cdot \frac{w + 1}{w - 1} + K

(\frac{w + 1}{w - 1})^{2} = \frac{w ^{2} + 2 w + 1}{w ^{2} - 2 w + 1}

3 \cdot \frac{w + 1}{w - 1} = \frac{3 w + 3}{w - 1}

= \frac{w ^{2} + 2 w + 1}{w ^{2} - 2 w + 1} + \frac{3 w + 3}{w - 1} + K

分解

w^{2} - 2 w + 1 : (w - 1)^{2}

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

(w - 1)^{2}, w - 1

的最小公倍数:

(w - 1)^{2}

根据最小公倍数调整分式

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

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

(w - 1)^{2} = w^{2} - 2 w + 1

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

乘开

w^{2} + 2 w + 1 + (3 w + 3) (w - 1) : 4 w^{2} + 2 w - 2

= K + \frac{4 w ^{2} + 2 w - 2}{w ^{2} - 2 w + 1}

流行的例子

化简 x(1+x/(10))

s im pl i f y x (1 + \frac{x}{10})

展开 (y-x+xycot(x))dx+xdy

e x p an d (y - x + x y cot (x)) d x + x d y

化简 (x-sqrt(y))(x+sqrt(y))

s im pl i f y (x - y) (x + y)

(\partial)/(\partial x)(({f}(x))(x-2)^2)

\frac{\partial}{\partial x} ((f (x)) (x - 2)^{2})

展开 (4(x^2-4x-1))/((x-1)^2(x+3)^2)

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