In Exercises 61–66, find all values of x satisfying the given conditions.y1 = (2x - 1)/(x^2 + 2x - 8), y2 = 2/(x + 4), y3 = 1/(x - 2), and y1 + y2 = y3.

Rational functions are expressions formed by the ratio of two polynomials. Understanding their behavior, including asymptotes and discontinuities, is crucial for solving equations involving them. In this question, the functions y1, y2, and y3 are rational, and their properties will influence the solutions for x.

To combine rational expressions, finding a common denominator is essential. This process allows for the addition or subtraction of fractions, which is necessary when setting y1 + y2 equal to y3. Mastery of this concept is vital for simplifying the equation and solving for x.

Solving rational equations involves isolating the variable and eliminating denominators, often by multiplying through by the least common denominator. This step is crucial to avoid undefined values and to find valid solutions for x. Understanding how to manipulate and solve these equations is key to answering the given problem.