Question

What is the correct form of the partial fraction decomposition for the expression 24/(x+6)(x−4)?

a. A/x+6 + B/x−4
b. B/x+6 + A/x−4
c. A/x+6 − B/x−4
d. B/x+6 − A/x−4​

Answer 1

The correct form of partial fraction decomposition for the expression given is option a. A/x+6 + B/x-4. This is determined through the method of setting up equations to solve for coefficients A and B.

Step-by-step explanation:

The correct form of the partial fraction decomposition for the expression 24/(x+6)(x−4) is a. A/x+6 + B/x−4. To determine this, we assign coefficients A and B to each of the denominators such that when combined, they equal the original fraction. Following the partial fraction decomposition method, we set up the equation 24/(x+6)(x−4) = A/(x+6) + B/(x−4) and find the values of A and B that satisfy the equality. By directly comparing the coefficients or by plugging in specific values for x that simplify the equation, we can solve for A and B.

This process involves cross-multiplication and, potentially, solving a system of equations to find the values for A and B which, when substituted back into the partial fractions, yield the correct decomposed form of the given rational expression.