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人気のある代数 >

x/(ab)+x/(bc)+x/(ca)-1=abc-x(a+b+c)

解

\frac{x}{ab} + \frac{x}{b c} + \frac{x}{c a} - 1 = ab c - x (a + b + c)

解

x = \frac{a ^{2} b ^{2} c ^{2} + ab c}{c + a + b + a ^{2} b c + a b ^{2} c + ab c ^{2}}; ab c \neq = 0, a \neq = \frac{- 1 - b ^{2} c - b c ^{2} + b ^{4} c ^{2} + 2 b ^{3} c ^{3} + b ^{2} c ^{4} - 2 b ^{2} c - 2 b c ^{2} + 1}{2 b c}, a \neq = \frac{- 1 - b ^{2} c - b c ^{2} - b ^{4} c ^{2} + 2 b ^{3} c ^{3} + b ^{2} c ^{4} - 2 b ^{2} c - 2 b c ^{2} + 1}{2 b c}

解答ステップ

\frac{x}{ab} + \frac{x}{b c} + \frac{x}{c a} - 1 = ab c - x (a + b + c)

LCMで乗じる

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

拡張

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

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

ab c

を右側に移動します

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

両辺から

- a^{2} b c x - a b^{2} c x - ab c^{2} x

を引く

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

簡素化

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

因数

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

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

以下で両辺を割る

c + a + b + a^{2} b c + a b^{2} c + ab c^{2}; ab c \neq = 0, a \neq = \frac{- 1 - b ^{2} c - b c ^{2} + b ^{4} c ^{2} + 2 b ^{3} c ^{3} + b ^{2} c ^{4} - 2 b ^{2} c - 2 b c ^{2} + 1}{2 b c}, a \neq = \frac{- 1 - b ^{2} c - b c ^{2} - b ^{4} c ^{2} + 2 b ^{3} c ^{3} + b ^{2} c ^{4} - 2 b ^{2} c - 2 b c ^{2} + 1}{2 b c}

x = \frac{a ^{2} b ^{2} c ^{2} + ab c}{c + a + b + a ^{2} b c + a b ^{2} c + ab c ^{2}}; ab c \neq = 0, a \neq = \frac{- 1 - b ^{2} c - b c ^{2} + b ^{4} c ^{2} + 2 b ^{3} c ^{3} + b ^{2} c ^{4} - 2 b ^{2} c - 2 b c ^{2} + 1}{2 b c}, a \neq = \frac{- 1 - b ^{2} c - b c ^{2} - b ^{4} c ^{2} + 2 b ^{3} c ^{3} + b ^{2} c ^{4} - 2 b ^{2} c - 2 b c ^{2} + 1}{2 b c}

グラフ

人気の例

\frac{4 x + 5}{3} = 11

16 = \frac{1}{4} h

(2x-3)/2 =(4x)/3

\frac{2 x - 3}{2} = \frac{4 x}{3}

20 - 4 x = 16

6 (x - 4) 2 + 40 = 16