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受欢迎的代数 >

(x-a-b)/c+(x-b-c)/a+(x-c-a)/b =3

解答

\frac{x - a - b}{c} + \frac{x - b - c}{a} + \frac{x - c - a}{b} = 3

解答

x = \frac{3 ab c + a ^{2} b + a b ^{2} + b ^{2} c + b c ^{2} + a c ^{2} + a ^{2} c}{ab + b c + a c}; ab c \neq = 0, a \neq = - \frac{b c}{b + c}

求解步骤

\frac{x - a - b}{c} + \frac{x - b - c}{a} + \frac{x - c - a}{b} = 3

乘以最小公倍数

ab (x - a - b) + b c (x - b - c) + a c (x - c - a) = 3 ab c; ab c \neq = 0

乘开

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

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

乘开

b c (x - b - c) : b c x - b^{2} c - b c^{2}

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

乘开

a c (x - c - a) : a c x - a c^{2} - a^{2} c

ab x - a^{2} b - a b^{2} + b c x - b^{2} c - b c^{2} + a c x - a c^{2} - a^{2} c = 3 ab c; ab c \neq = 0

将

a^{2} b

到右边

ab x - a b^{2} + b c x - b^{2} c - b c^{2} + a c x - a c^{2} - a^{2} c = 3 ab c + a^{2} b; ab c \neq = 0

将

a b^{2}

到右边

ab x + b c x - b^{2} c - b c^{2} + a c x - a c^{2} - a^{2} c = 3 ab c + a^{2} b + a b^{2}; ab c \neq = 0

将

b^{2} c

到右边

ab x + b c x - b c^{2} + a c x - a c^{2} - a^{2} c = 3 ab c + a^{2} b + a b^{2} + b^{2} c; ab c \neq = 0

将

b c^{2}

到右边

ab x + b c x + a c x - a c^{2} - a^{2} c = 3 ab c + a^{2} b + a b^{2} + b^{2} c + b c^{2}; ab c \neq = 0

将

a c^{2}

到右边

ab x + b c x + a c x - a^{2} c = 3 ab c + a^{2} b + a b^{2} + b^{2} c + b c^{2} + a c^{2}; ab c \neq = 0

将

a^{2} c

到右边

ab x + b c x + a c x = 3 ab c + a^{2} b + a b^{2} + b^{2} c + b c^{2} + a c^{2} + a^{2} c; ab c \neq = 0

分解

ab x + b c x + a c x : x (ab + b c + a c)

x (ab + b c + a c) = 3 ab c + a^{2} b + a b^{2} + b^{2} c + b c^{2} + a c^{2} + a^{2} c; ab c \neq = 0

两边除以

ab + b c + a c; ab c \neq = 0, a \neq = - \frac{b c}{b + c}

x = \frac{3 ab c + a ^{2} b + a b ^{2} + b ^{2} c + b c ^{2} + a c ^{2} + a ^{2} c}{ab + b c + a c}; ab c \neq = 0, a \neq = - \frac{b c}{b + c}

作图

流行的例子

\frac{2 x + 2}{3} = 1

-{3x+8-[-15+6x-(-3x+2)-(5x+4)-29]}=-5

- {3 x + 8 - [- 15 + 6 x - (- 3 x + 2) - (5 x + 4) - 29]} = - 5

solvefor x,v=(Dx)/(Dt)

so l v e f or x, v = \frac{D x}{D t}

2(x-3)+3(x-5)=5(x-8)

2 (x - 3) + 3 (x - 5) = 5 (x - 8)

solvefor a,h=(at)/(sqrt(1-e^{2t))}

so l v e f or a, h = \frac{a t}{1 - e ^{2 t}}