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受欢迎的代数 >

化简 (x-c)/(a+b)+(x-b)/(a+c)+(x-a)/(b+c)

解答

化简

\frac{x - c}{a + b} + \frac{x - b}{a + c} + \frac{x - a}{b + c}

解答

\frac{- c ^{3} + x c ^{2} - c ^{2} b - c ^{2} a + x b ^{2} - a b ^{2} - c b ^{2} + x a ^{2} - c a ^{2} - a ^{2} b + 3 c b x + 3 c a x + 3 ab x - 3 c ab - b ^{3} - a ^{3}}{( a + b ) ( c + a ) ( c + b )}

求解步骤

\frac{x - c}{a + b} + \frac{x - b}{a + c} + \frac{x - a}{b + c}

a + b, a + c, b + c

的最小公倍数:

(a + b) (c + a) (c + b)

根据最小公倍数调整分式

= \frac{( x - c ) ( c + a ) ( c + b )}{( a + b ) ( c + a ) ( c + b )} + \frac{( x - b ) ( a + b ) ( c + b )}{( a + b ) ( c + a ) ( c + b )} + \frac{( x - a ) ( a + b ) ( c + a )}{( a + b ) ( c + a ) ( c + b )}

使用分式法则:

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

= \frac{( x - c ) ( c + a ) ( c + b ) + ( x - b ) ( a + b ) ( c + b ) + ( x - a ) ( a + b ) ( c + a )}{( a + b ) ( c + a ) ( c + b )}

化简

(x - c) (c + a) (c + b) + (x - b) (a + b) (c + b) + (x - a) (a + b) (c + a) : - c^{3} + x c^{2} - c^{2} b - c^{2} a + x b^{2} - a b^{2} - c b^{2} + x a^{2} - c a^{2} - a^{2} b + 3 c b x + 3 c a x + 3 ab x - 3 c ab - b^{3} - a^{3}

= \frac{- c ^{3} + x c ^{2} - c ^{2} b - c ^{2} a + x b ^{2} - a b ^{2} - c b ^{2} + x a ^{2} - c a ^{2} - a ^{2} b + 3 c b x + 3 c a x + 3 ab x - 3 c ab - b ^{3} - a ^{3}}{( a + b ) ( c + a ) ( c + b )}

流行的例子

化简 (1/3-6m)-(1/4 n-8)

s im pl i f y (\frac{1}{3} - 6 m) - (\frac{1}{4} n - 8)

化简 (7!)/((7-2)!)

s im pl i f y \frac{7 !}{( 7 - 2 ) !}

化简 1-1/(x+1)

s im pl i f y 1 - \frac{1}{x + 1}

化简 10^{0.7}

s im pl i f y 1 0^{0.7}

展开 (2x-6)(3x-2)

e x p an d (2 x - 6) (3 x - 2)