Learning Objectives:

__Math Tutoring on Performing Partial Fraction Decomposition__

The process of considering a **rational expression** and **decomposing **or** breaking **it into simpler **rational expressions** that we can add or subtract to get the original **rational expression** is called **partial fraction decomposition**. If the degree of the numerator is greater than or equal to the degree of the denominator, we perform **long division.**

** Step 1:** Factor the denominator into **prime linear or quadratic factors**.

**Step 2:** **Linear Factors:** Each distinct **linear factor** of the form **(px + q)** include the term **A/ (ax + b).** For each repeated factor **(ax + b)ᵑ** we must include** n** terms of the form : **A/ (ax + b) + B/(ax + b)² + C/(ax + b )³ + ………………**

In general we have added and simplified **rational expressions**. **Partial-fraction decomposition** is the process of starting with the simplified answer and taking it back apart, of **"decomposing"** the final expression into its initial **polynomial fractions.**

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**Hook Questions:**

*1. **How do you decompose a fraction?*

*2. **What is the partial derivative?*

*3. **How do you complete the square?*

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