In Exercises 61–66, find all values of x satisfying the given conditions.y1 = 5/(x + 4), y2 = 3/(x + 3), y3 = (12x + 19)/(x^2 + 7x + 12). and y1 + y2 = y3.

Rational functions are expressions formed by the ratio of two polynomials. In this question, y1, y2, and y3 are rational functions where the numerator and denominator are polynomials. Understanding how to manipulate and combine these functions is essential for solving the equation y1 + y2 = y3.

To add or equate rational functions, it is often necessary to find a common denominator. This involves identifying a common multiple of the denominators of the functions involved, which allows for the combination of the fractions into a single expression. This step is crucial for simplifying the equation and solving for x.

Once the rational functions are combined, the resulting equation will typically be a polynomial equation. Solving polynomial equations involves finding the values of x that satisfy the equation, which may require factoring, using the quadratic formula, or applying other algebraic techniques. This is the final step in determining the values of x that meet the given conditions.