展开 (x+2)/(2-x-12)+(x-1)/(2+2x)

解答

展开

\frac{x + 2}{2 - x - 12} + \frac{x - 1}{2 + 2 x}

\frac{x ^{2} - 3 x + 14}{- 2 x ^{2} - 22 x - 20}

求解步骤

\frac{x + 2}{2 - x - 12} + \frac{x - 1}{2 + 2 x}

2 - x - 12 = - x - 10

= \frac{x + 2}{- x - 10} + \frac{x - 1}{2 x + 2}

分解

2 x + 2 : 2 (x + 1)

= \frac{x + 2}{- x - 10} + \frac{x - 1}{2 ( x + 1 )}

- x - 10, 2 (x + 1)

的最小公倍数:

2 (x + 1) (- x - 10)

根据最小公倍数调整分式

= \frac{( x + 2 ) \cdot 2 ( x + 1 )}{( - x - 10 ) \cdot 2 ( x + 1 )} + \frac{( x - 1 ) ( - x - 10 )}{2 ( x + 1 ) ( - x - 10 )}

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{( x + 2 ) \cdot 2 ( x + 1 ) + ( x - 1 ) ( - x - 10 )}{2 ( x + 1 ) ( - x - 10 )}

乘开

2 (x + 1) (- x - 10) : - 2 x^{2} - 22 x - 20

= \frac{2 ( x + 2 ) ( x + 1 ) + ( x - 1 ) ( - x - 10 )}{- 2 x ^{2} - 22 x - 20}

乘开

(x + 2) \cdot 2 (x + 1) + (x - 1) (- x - 10) : x^{2} - 3 x + 14

= \frac{x ^{2} - 3 x + 14}{- 2 x ^{2} - 22 x - 20}

e x p an d t^{2} e^{4 t^{5}} (3 - 20 t^{5} - 40 t^{2})

s im pl i f y 8 (sin (2 x) - cos (2 x))

e x p an d l im x \Rightarrow - 1 (x^{3} - 2 x^{2} - 5 x - 1)

e x p an d π (1 + \frac{3}{5})

e x p an d y^{''} (x) - (x + 1) y