Final answer:
To find the difference between the two given fractions, identify a common denominator, rewrite each fraction with the common denominator, subtract the second fraction from the first, and simplify the result.
Step-by-step explanation:
To find the difference between the fractions (7)/(x²+4x) and (5)/(x²-16), you first need to identify a common denominator. Given that x²-16 is a difference of squares, it can be factored into (x+4)(x-4). The common denominator will then be (x+4)(x-4)(x+4) or (x+4)²(x-4).
After rewriting each fraction with this common denominator, subtract the second fraction from the first and simplify the expression. This process involves algebraic manipulations such as factoring, finding common denominators, expanding expressions, and simplifying.
If the question extends to finding the value for which the expression is defined, you might utilize the quadratic equation or complete the square method to find the values of x that satisfy the equation obtained from the difference.