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A root of the equation (a+c)/(x+a)+(b...

A root of the equation `(a+c)/(x+a)+(b+c)/(x+b)=(2(a+b+c))/(x+a+b)` is

A

a

B

b

C

c

D

a+b+c

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \[ \frac{a+c}{x+a} + \frac{b+c}{x+b} = \frac{2(a+b+c)}{x+a+b} \] we will follow these steps: ### Step 1: Clear the denominators Multiply both sides of the equation by \((x+a)(x+b)(x+a+b)\) to eliminate the denominators: \[ (a+c)(x+b)(x+a+b) + (b+c)(x+a)(x+a+b) = 2(a+b+c)(x+a)(x+b) \]
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