In this video I over an introduction on partial fraction decomposition and go over some general techniques in decomposing a rational function that has unique linear factors in the denominator. Rational functions in this form are pretty straight forward to decompose but sometimes the denominator contains repeating and/or non-linear factors. For these cases the decomposition method is a bit more complicated and I will cover these in my later videos.

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Partial Fraction Decomposition: General Techniques

Partial fraction decomposition is the process of breaking down rational functions (ratios of polynomials) into simpler functions, called partial fractions.

If we start from simple rational functions such as:

Now Partial fractions decomposition is starting from the function in the right hand side and breaking it apart by working backwards:

First step in decomposing a rational function is by first factoring the denominator:

Now we write the partial fractions with one of the factors for each of the denominators. But since we don't know what the numerators are yet, we assign them letters:

Then we equate the 2 sides and then have to solve for A and B:

Another way of solving for A and B is by choosing values of x and simply solving for A and B.

Note: In this example the denominator factored into unique linear factors:

Decomposing rational functions of this type are pretty straight forward. In later videos I will go over the cases where the factors repeat and/or have non-linear factors such: