Multiple choice

A root of equation $\displaystyle \frac{a+c}{x+a}+\frac{b+c}{x+b}=\frac{2(a+b+c)}{x+a+b}$ is

  1. $a$
  2. $b$
  3. $c$
  4. $a+b+c$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Testing x = c: (a+c)/(c+a) + (b+c)/(c+b) = 1 + 1 = 2. The RHS is 2(a+b+c)/(c+a+b) = 2(a+b+c)/(a+b+c) = 2. Since LHS = RHS, x = c is a root.

AI explanation

Substitute x = c into the given equation: (a+c)/(c+a) + (b+c)/(c+b) = 2(a+b+c)/(c+a+b). Both sides simplify to 1 + 1 = 2, proving that x = c satisfies the equality. Therefore, c is a valid root of the equation.

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