展开 (3(2x-1)^2)/(2x)

解答

展开

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

6 x - 6 + \frac{3}{2 x}

求解步骤

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

(2 x - 1)^{2} = 4 x^{2} - 4 x + 1

= \frac{3 ( 4 x ^{2} - 4 x + 1 )}{2 x}

乘开

3 (4 x^{2} - 4 x + 1) : 12 x^{2} - 12 x + 3

= \frac{12 x ^{2} - 12 x + 3}{2 x}

使用分式法则:

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

\frac{12 x ^{2} - 12 x + 3}{2 x} = \frac{12 x ^{2}}{2 x} - \frac{12 x}{2 x} + \frac{3}{2 x}

= \frac{12 x ^{2}}{2 x} - \frac{12 x}{2 x} + \frac{3}{2 x}

消掉

\frac{12 x ^{2}}{2 x} : 6 x

= 6 x - \frac{12 x}{2 x} + \frac{3}{2 x}

消掉

\frac{12 x}{2 x} : 6

= 6 x - 6 + \frac{3}{2 x}

e x p an d \frac{3 x ^{2} - 6 x + 2}{2 ( 4 - 3 y ^{2} + 2 y ^{3} - 4 y )}

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

e x p an d x d x + (y - 2 x) d y

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

e x p an d \frac{- cot ( x ) csc ( x ) ( 1 + sec ( x ) ) - sec ( x ) tan ( x ) ( 1 + csc ( x ) )}{( 1 + sec ( x ) ) ^{2}}