how to turn a fraction in the form of (x + a)/(x + b)^2 into partial fractions?

Many students at first will incorrectly separate the fraction into two fractions in the form of A/(x + b) + B/(x + b). If we then multiplied the two back together we will find that it does not equate to the original fraction. We instead need to first create two fractions and equate them to the original one.(x + a)/(x + b)^2 = A/(x + b) + B/(x + b)^2Now we need to combine the two left hand fractions to create a single fraction. We do this by cross-multiplying.Once we have done that, we can start substituting in values to find the constants A and B. We can do this by subbing in x values that will cancel the other unknown out. Once we have one value of either A or B we can use that to find the other unknown, then we are done!