Final answer:
The question asks to simplify a complex rational expression which may lead to solving a quadratic equation using the quadratic formula (-b ± √(b² - 4ac)) / (2a).
Step-by-step explanation:
The question involves simplifying a complex rational expression and potentially solving a quadratic equation. When you have an expression such as (6x²+13x-5)/(X²-16) divided by (3x-1)/(X+4), you can simplify it by multiplying by the reciprocal of the second fraction. If this simplification leads to a quadratic equation, it can generally be solved using the quadratic formula, which is applicable to any equation of the form ax² + bx + c = 0. To solve for x, you would identify the coefficients a, b, and c, and substitute them into the formula (-b ± √(b² - 4ac)) / (2a). For some expressions, it might be necessary to expand the expression or multiply both sides by a common factor to simplify further or to transform it into an easier form for solving.