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人気のある代数 >

1/((a+b+c))= 1/a+1/b+1/x

解

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

解

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

解答ステップ

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

LCMで乗じる

ab x = a^{2} x + b^{2} x + 2 ab x + b c x + a c x + a b^{2} + a^{2} b + ab c

両辺から

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

を引く

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

簡素化

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

因数

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

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

以下で両辺を割る

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

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

グラフ

人気の例

((5x))/((x-3))+4/((x+3))=(90)/((x^2-9))

\frac{( 5 x )}{( x - 3 )} + \frac{4}{( x + 3 )} = \frac{90}{( x ^{2} - 9 )}

∣ x ∣ = \frac{1}{x}

solvefor s,1+(k_{c})/(((2s+1)(5s+1)))=0

so l v e f or s, 1 + \frac{k _{c}}{( ( 2 s + 1 ) ( 5 s + 1 ) )} = 0

x/((3-2x))=((x+1))/((3-x))

\frac{x}{( 3 - 2 x )} = \frac{( x + 1 )}{( 3 - x )}

ln(10/9)=(36*10^{10})/x

ln (\frac{10}{9}) = \frac{36 \cdot 1 0 ^{10}}{x}