The sum of roots of equation `1/(x+a)+1/(x+b)=1/c` is zero find the product of roots of equation a)0 b) `((a+b)/2)` c)`-((a^2+b^2)/2)` d) `2(a^2+b^2)`

Explanation

To solve the equation \( \frac{1}{x+a} + \frac{1}{x+b} = \frac{1}{c} \) and find the product of its roots given that the sum of the roots is zero, we can follow these steps:

### Step 1: Rewrite the equation
Start with the given equation:
\[ \frac{1}{x+a} + \frac{1}{x+b} = \frac{1}{c} \]
To combine the fractions on the left-hand side, find a common denominator:
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