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Solve for \(x\): \(\dfrac{a}{x-a} + \dfrac b{x-b} = \dfrac{2c}{x-c} \).

 Jan 16, 2021
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\(Solve for\ x:\\ \dfrac{a}{x-a} + \dfrac b{x-b} = \dfrac{2c}{x-c} \)

 

Hello Guest!

 

\(\dfrac{a(x-b)(x-c)+b(x-a)(x-c)}{(x-a)(x-b)(x-c)}=\dfrac{2c(x-a)(x-b)}{(x-a)(x-b)(x-c)}\)

 

\(a(x-b)(x-c)+b(x-a)(x-c)=2c(x-a)(x-b)\)

 

wolfram alpha  \(⇒ \)

\(2abc-2abx-acx+ax^2-bcx+bx^2=2abc-2acx-2bcx+2cx^2\) 

 

\(a+b-2c\neq0,\ x=\dfrac{2ab-ac-bc}{a+b+c}\)

\(b=a, c=a\)

 

\(x=0\)

laugh  !

 Jan 17, 2021
edited by asinus  Jan 17, 2021
edited by asinus  Jan 17, 2021

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