Final answer:
The student's question pertains to finding the partial fraction decomposition in calculus. The student must understand the division of exponentials as well as addition and subtraction of fractions in this context, using common denominators to simplify the expression for easier integration.
Step-by-step explanation:
The student is asked to find the partial fraction decomposition of an integrand. This technique is used in calculus to simplify complex rational expressions into simpler fractions that are easier to integrate. The process generally involves factoring the denominator and writing the integrand as a sum of fractions with unknown numerators. To solve for these numerators, we can equate coefficients or plug in convenient values of the variable after multiplying both sides by the common denominator.
When dealing with division of exponentials, which appears to be related to the question although insufficient context is given, the rule is to divide the coefficients (digit terms) and subtract the exponents if the bases are the same. For instance, in the expression ax / ay, the result would be ax-y because the terms have the same base.
Understanding addition and subtraction of fractions involves finding a common denominator. This common denominator is often the product of the denominators of the individual fractions, which allows us to add or subtract the numerators directly. Simplifying the resulting fraction can then be done by canceling out any common factors between the numerator and denominator.