7. What is the goal of the method of partial fractions?

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Welcome back everyone. Find decomposition in terms of arbitrary constants for the given rational expression x + 2 divided by x cubed minus 2 x 2 minus 3 x. For this problem, let's remember that first of all what we have to do is factor out the denominator so we can first of all factor out x to get x + 2 divided by x which is multiplied by x2 minus 2 x minus 3. This allows us to now factor the quadratic part, which gives us x + 2 divided by x and x 2 minus 2 x minus 3 becomes x minus 3. Multiplied by x plus 1. Notice that now we have 3 linear factors in the denominator, and according to the rule, what we want to do is simply add 3 fractions. Each fraction is going to contain a constant in the numerator. Let's call the first constant an arbitrary constant a. It is going to be divided by the first linear factor X. We're going to add a positive sign to add the second fraction which will consist of b. This is another arbitrary constant divided by the second linear factor x minus 3. And finally we're going to add the 3rd arbitrary constant c divided by the final linear factor x + 1. This is how we arrive at the final answer for this problem. We're not required to find A, B, and C. Thank you for watching.

7. What is the goal of the method of partial fractions?

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