Question

(x)/((x+5)(x-3)) What is the partial fraction decomposition?

Answer 1

To decompose the fraction (x)/((x+5)(x-3)) into partial fractions, follow the steps: find the values of the constants A and B, set up the equation, and solve for the values of A and B. The partial fraction decomposition is (3/(x+5)) - (2/(x-3)).

Step-by-step explanation:

To decompose the fraction (x)/((x+5)(x-3)) into partial fractions, we first factor the denominator as (x+5)(x-3). The numerator has a degree of 1 and the denominator has a degree of 2, which means we can write the fraction as a sum of two fractions with simpler denominators.

1. Step 1: Find the values of the constants A and B.
2. Step 2: Set up the equation by setting the numerator equal to the sum of the two partial fractions.
3. Step 3: Solve for the values of A and B by equating the coefficients of the corresponding powers of x.

So the partial fraction decomposition of (x)/((x+5)(x-3)) is (3/(x+5)) - (2/(x-3)).