展开 ((d(b-x)(y-x)))/y

解答

展开

\frac{( d ( b - x ) ( y - x ) )}{y}

d b - \frac{d b x}{y} - d x + \frac{d x ^{2}}{y}

求解步骤

\frac{d ( b - x ) ( y - x )}{y}

乘开

d (b - x) (y - x) : d b y - d b x - d x y + d x^{2}

= \frac{d b y - d b x - d x y + d x ^{2}}{y}

使用分式法则:

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

\frac{d b y - d b x - d x y + d x ^{2}}{y} = \frac{d b y}{y} - \frac{d b x}{y} - \frac{d x y}{y} + \frac{d x ^{2}}{y}

= \frac{d b y}{y} - \frac{d b x}{y} - \frac{d x y}{y} + \frac{d x ^{2}}{y}

消掉

\frac{d b y}{y} : d b

= d b - \frac{d b x}{y} - \frac{d x y}{y} + \frac{d x ^{2}}{y}

消掉

\frac{d x y}{y} : d x

= d b - \frac{d b x}{y} - d x + \frac{d x ^{2}}{y}

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

s im pl i f y (\frac{b}{y} + x) (\frac{b}{y} - x)

e x p an d (ux - 2 x) (u d x + x d u)

e x p an d (4 - 2) (3 - 3, - 2 - 4) (x, y)

s im pl i f y (sin (θ) + i cos (θ))^{3}