化简 3/(x+1)+5/(x^2-2x-3)

解答

化简

\frac{3}{x + 1} + \frac{5}{x ^{2} - 2 x - 3}

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

求解步骤

\frac{3}{x + 1} + \frac{5}{x ^{2} - 2 x - 3}

x + 1, x^{2} - 2 x - 3

的最小公倍数:

(x + 1) (x - 3)

根据最小公倍数调整分式

= \frac{3 ( x - 3 )}{( x + 1 ) ( x - 3 )} + \frac{5}{( x + 1 ) ( x - 3 )}

使用分式法则:

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

= \frac{3 ( x - 3 ) + 5}{( x + 1 ) ( x - 3 )}

化简

3 (x - 3) + 5 : 3 x - 4

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

s im pl i f y sin^{2} (x) + sin^{2} (x) cot^{2} (x)

e x p an d 3 a (8 a - 6 b)

s im pl i f y - a^{4} + 4 - 9 a^{4} - 3 - 4 a^{2}

s im pl i f y \frac{a ^{2} + 2 a - 3}{a ^{2} + 4 a - 5}

s im pl i f y \frac{- cos ( x )}{sin ( x )}