Problem 58 - Algebra and Trigonometry

Question

How can you verify your result for the partial fraction decomposition for a given rational expression without using a graphing utility?

Step-by-Step Solution

Answer

To verify a result for a partial fraction decomposition, decompose the rational expression to partial fractions. Then, recombine these partial fractions. If the recombined version matches the original function, the decomposition is correct.

Step 1 - Understand the Problem

You've been asked to verify a result for the partial fraction decomposition of a rational expression. That means you first need to determine the partial fractions.

Step 2 - Decompose into Partial Fractions

Find a partial fraction decomposition of the given rational expression. This is typically done by creating a system of equations based on the coefficients of the polynomials after you split up the fraction and then solving that system.

Step 3 - Verify the Decomposition

Now that you've found your partial fractions, you need to confirm your work is correct. Do so by recombining the partial fractions and simplifying to see if the result is the original rational function.

Step 4 - Check work

If your recombined and simplified result matches the original rational function, then you've successfully demonstrated how to verify a partial fraction decomposition without a graphing utility.