zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

化简 a/(a+b)-b/(a-b)+1/(a^2-b^2)

解答

化简

\frac{a}{a + b} - \frac{b}{a - b} + \frac{1}{a ^{2} - b ^{2}}

解答

\frac{a ^{4} - a ^{2} b ^{2} - 2 a ^{3} b + 2 a b ^{3} + b ^{4} - b ^{2} a ^{2} + a ^{2} - b ^{2}}{( a + b ) ( a - b ) ( a ^{2} - b ^{2} )}

求解步骤

\frac{a}{a + b} - \frac{b}{a - b} + \frac{1}{a ^{2} - b ^{2}}

a + b, a - b, a^{2} - b^{2}

的最小公倍数:

(a + b) (a - b) (a^{2} - b^{2})

根据最小公倍数调整分式

= \frac{a ( a - b ) ( a ^{2} - b ^{2} )}{( a + b ) ( a - b ) ( a ^{2} - b ^{2} )} - \frac{b ( a + b ) ( a ^{2} - b ^{2} )}{( a + b ) ( a - b ) ( a ^{2} - b ^{2} )} + \frac{( a + b ) ( a - b )}{( a + b ) ( a - b ) ( a ^{2} - b ^{2} )}

使用分式法则:

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

= \frac{a ( a - b ) ( a ^{2} - b ^{2} ) - b ( a + b ) ( a ^{2} - b ^{2} ) + ( a + b ) ( a - b )}{( a + b ) ( a - b ) ( a ^{2} - b ^{2} )}

化简

a (a - b) (a^{2} - b^{2}) - b (a + b) (a^{2} - b^{2}) + (a + b) (a - b) : a^{4} - a^{2} b^{2} - 2 a^{3} b + 2 a b^{3} + b^{4} - b^{2} a^{2} + a^{2} - b^{2}

= \frac{a ^{4} - a ^{2} b ^{2} - 2 a ^{3} b + 2 a b ^{3} + b ^{4} - b ^{2} a ^{2} + a ^{2} - b ^{2}}{( a + b ) ( a - b ) ( a ^{2} - b ^{2} )}

流行的例子

∣ 3 x + 10 ∣ = ∣ x - 17 ∣

∣ x - 3 ∣ = 2

化简 (pi/4)/(2pi)

s im pl i f y \frac{\frac{π}{4}}{2 π}

x^{2} - 10 x + 6 = 0

x - x = 0