Be sure to pay close attention in distributing the numerator and be very careful when plugging in the numbers into the calculator. Also, remember to use the rref feature and check if the answers are correct.
Part 1: First, you would have to find the common denominator. In this case it's (x+4)(x-2)(x+1). Then, you distribute them to the numerator but remember to foil it out first. Once you have completed this step, you add up all the like terms.
Part 2: Now you have to replace the numerator with letter values. Then, you multiply by the common denominator again. This time, instead of distributing a number, you'll be distributing a letter. Next, you set the distributed product equal to the original and add up any like terms (like terms highlighted in above picture). After, you've found the like terms, you can start canceling out and the end product will be the system (as shown above).
Part 3 : The last step is to plug in the system into the calculator. Then you use the rref feature to find your answer. Once you have found what A,B, and C equals, plug them back into the original 3 fractions.