1. **State the problem:** Solve the rational equation given (though the exact equation is not provided, we will outline the general approach). 2. **General formula and rules:** A rational equation is an equation that involves fractions with polynomials in the numerator and denominator. To solve it, we: - Find the least common denominator (LCD) of all fractions. - Multiply both sides of the equation by the LCD to eliminate denominators. - Solve the resulting polynomial equation. - Check for extraneous solutions by ensuring no denominator is zero. 3. **Step-by-step solution:** - Identify denominators and find the LCD. - Multiply every term by the LCD. - Simplify and solve the resulting equation. - Verify solutions against original denominators. 4. **Example:** Suppose the equation is $$\frac{1}{x} + \frac{2}{x+1} = \frac{3}{x(x+1)}$$ - LCD is $$x(x+1)$$. - Multiply both sides by $$x(x+1)$$: $$x(x+1) \cdot \frac{1}{x} + x(x+1) \cdot \frac{2}{x+1} = x(x+1) \cdot \frac{3}{x(x+1)}$$ - Simplify: $$(x+1) + 2x = 3$$ - Combine like terms: $$x + 1 + 2x = 3$$ $$3x + 1 = 3$$ - Solve for $$x$$: $$3x = 2$$ $$x = \frac{2}{3}$$ - Check denominators: $$x \neq 0$$ and $$x \neq -1$$, so $$x=\frac{2}{3}$$ is valid. 5. **Final answer:** $$x=\frac{2}{3}$$ This method applies to any rational equation: clear denominators, solve the polynomial, and check for extraneous solutions.