Student Problem #5

This is picture shows my example of solving a partial fraction decomposition with distinct factors. To solve a partial fraction decomposition with distinct factors problem, first you have to factor the denominator if possible or if not already done (x * x+1 * x-1). Then for each factor, use a letter beginning with A as your numerator and the factor as your denominator (A/x, B/x+1, C/x-1). Next, you have to add these new fractions with each other (A/x + B/x+1 + C/x-1) and set it equal to the original fraction. Now you would need the same denominator to go any further so multiply each fraction with whats missing and you will get like terms. Simplify these like terms and turn it into a system. Solve the system and the substitute the answers with the letters of the fraction.