What is the answer to a/((x-a))+b/((x-b))=2 c/((x-c)) ?

The answer to a/((x-a))+b/((x-b))=2 c/((x-c)) is x=0,x=-(-2ab+ac+bc)/(a+b-2c);\quad a+b-2c\ne 0

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

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

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

Solution steps

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

Multiply by LCM

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

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = c

Combine undefined points with solutions:

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

a^{2} = a^{- 2}

8400 x^{- 1} = 1 mod 11

\frac{( x + 8 )}{x} = e^{3}

\frac{1.5}{3} = \frac{1}{x}

a, \frac{a}{b} + c + \frac{b}{c} + a + \frac{c}{a} + b = 0

What is the answer to a/((x-a))+b/((x-b))=2 c/((x-c)) ?
The answer to a/((x-a))+b/((x-b))=2 c/((x-c)) is x=0,x=-(-2ab+ac+bc)/(a+b-2c);\quad a+b-2c\ne 0