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受欢迎的代数 >

化简 (a-b)/(3a+3b)-(a-2b)/(6a-6b)+(a^2+2ab-6b^2)/(9a^2-9b^2)

解答

化简

\frac{a - b}{3 a + 3 b} - \frac{a - 2 b}{6 a - 6 b} + \frac{a ^{2} + 2 ab - 6 b ^{2}}{9 a ^{2} - 9 b ^{2}}

解答

\frac{5 a}{18 ( a + b )}

求解步骤

\frac{a - b}{3 a + 3 b} - \frac{a - 2 b}{6 a - 6 b} + \frac{a ^{2} + 2 ab - 6 b ^{2}}{9 a ^{2} - 9 b ^{2}}

3 a + 3 b, 6 a - 6 b, 9 a^{2} - 9 b^{2}

的最小公倍数:

(3 a + 3 b) (6 a - 6 b) (9 a^{2} - 9 b^{2})

根据最小公倍数调整分式

= \frac{( a - b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )}{( 3 a + 3 b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )} - \frac{( a - 2 b ) ( 3 a + 3 b ) ( 9 a ^{2} - 9 b ^{2} )}{( 3 a + 3 b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )} + \frac{( a ^{2} + 2 ab - 6 b ^{2} ) ( 3 a + 3 b ) ( 6 a - 6 b )}{( 3 a + 3 b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )}

使用分式法则:

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

= \frac{( a - b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} ) - ( a - 2 b ) ( 3 a + 3 b ) ( 9 a ^{2} - 9 b ^{2} ) + ( a ^{2} + 2 ab - 6 b ^{2} ) ( 3 a + 3 b ) ( 6 a - 6 b )}{( 3 a + 3 b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )}

化简

(a - b) (6 a - 6 b) (9 a^{2} - 9 b^{2}) - (a - 2 b) (3 a + 3 b) (9 a^{2} - 9 b^{2}) + (a^{2} + 2 ab - 6 b^{2}) (3 a + 3 b) (6 a - 6 b) : 45 a^{4} - 45 a^{2} b^{2} - 45 a^{3} b + 45 a b^{3}

= \frac{45 a ^{4} - 45 a ^{2} b ^{2} - 45 a ^{3} b + 45 a b ^{3}}{( 3 a + 3 b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )}

消掉

\frac{45 a ^{4} - 45 a ^{2} b ^{2} - 45 a ^{3} b + 45 a b ^{3}}{( 3 a + 3 b ) ( 6 a - 6 b ) ( 9 a ^{2} - 9 b ^{2} )} : \frac{5 a}{18 ( a + b )}

= \frac{5 a}{18 ( a + b )}

流行的例子

化简 (3x+2y)(3x+2y)

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s im pl i f y 4 \cdot (- 9)

化简 2/2+2/3+2/4+2/5+2/6+2/7+2/8+2/9

s im pl i f y \frac{2}{2} + \frac{2}{3} + \frac{2}{4} + \frac{2}{5} + \frac{2}{6} + \frac{2}{7} + \frac{2}{8} + \frac{2}{9}

展开 (x^2+y^2+1)^2

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

展开 (x-8)(x-1)

e x p an d (x - 8) (x - 1)