Final answer:
The student's mathematics question involves solving a rational equation and determining its domain, which is typically done by factoring or using the quadratic formula, and by excluding the values where the denominator equals zero.
Step-by-step explanation:
The student's question involves solving a rational equation and specifying its domain. The equation provided appears to be incomplete, but oftentimes to solve a rational equation, you would first find a common denominator, combine the fractions, and then solve for 'x'. It's important to note that the domain of a rational equation excludes values that would make the denominator zeroTo specify the domain of the given rational equation, we need to determine where the denominator is not equal to zero. Given the denominators (x+4), (x-4), and (x²-16), we can set each equal to zero and solve for 'x'. This gives us the values that cannot be part of the domain. In this case, x²-16 factors to (x+4)(x-4), indicating that x cannot be 4 or -4Finding the solution to the equation would involve combining the fractions over the common denominator (x²-16),
simplifying and then solving the resulting equation, likely using methods such as factoring or the quadratic formula, depending on the rearrangement of the terms.To solve the rational equation (2)/(x+4) - (3)/(x-4) = (4)/(x^2-16), we need to find the values of x that satisfy this equation. First, we need to determine the domain of the equation. Since the denominator cannot be equal to zero, we exclude any values of x that would make the denominators equal to zeroThe domain of the equation is x ≠ -4, x ≠ 4.Next, we can simplify the equation by finding a common denominatorMultiplying both sides of the equation by (x+4)(x-4) will eliminate the denominators, resulting in a polynomial equation that can be solved.After multiplying and simplifying, the equation becomes 2(x-4) - 3(x+4) = 4.Solving this equation step by step, we get the solution x = -12.Therefore, the solution to the rational equation is x = -12, and the domain of the equation is x ≠ -4, x ≠ 4.