1. The problem is to simplify the algebraic fraction expression: \( \frac{a}{14} + \frac{b}{14} = \frac{a}{2x} + \frac{b}{2x} = \frac{c}{x} + \frac{y}{5x} \). 2. We use the rule that fractions with the same denominator can be added by adding their numerators: \( \frac{m}{n} + \frac{p}{n} = \frac{m+p}{n} \). 3. Simplify the first sum: $$\frac{a}{14} + \frac{b}{14} = \frac{a+b}{14}$$ 4. Simplify the second sum: $$\frac{a}{2x} + \frac{b}{2x} = \frac{a+b}{2x}$$ 5. Simplify the third sum: $$\frac{c}{x} + \frac{y}{5x} = \frac{5c}{5x} + \frac{y}{5x} = \frac{5c + y}{5x}$$ 6. Final simplified expressions are: $$\frac{a+b}{14}, \quad \frac{a+b}{2x}, \quad \frac{5c + y}{5x}$$