Learning Objectives:

__Math Tutoring on Multiplying and Dividing Rational Expressions__

**Multiplying rational expressions** is just like **multiplying fractions.** So, the basic rule is to find the product of two** rational** **expressions**, you **multiply the numerators** together and then you **multiply the denominators** together. However, by now, we know our product must be in simplified form. Let **u, v, w **and** z** represent real numbers, variables or algebraic expressions such that **v ≠ 0 **and** z ≠ 0.** Then the product **u/v and w/z **is** u/v •w/z = uw/vz**.

So, in order to recognize the **common factors** in the product, we will write the numerators and denominators in factored form to simplify before we **multiply**. Let's go ahead and take a look at **division** now. The main thing to remember about the **division of rational expressions** is that we convert them to **multiplication**. Let **u, v, w, **and** z** represent real numbers, variables or algebraic expressions such that, **v ≠ 0 **and **z ≠ 0.** Then the quotient of **u/v** and **w/z** is **u/v ÷w/z = u/v • z/w =** **uz/vw.** So, instead of **dividing **by **w** over **z,** we will **multiply** by the reciprocal or **multiply** by** z** over **w**. Once we convert the problem to **multiplication**, we will follow the same steps as **multiplication**.

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**Hook Questions:**

*1. How do you multiply and divide rational expressions?*

*2. What are the steps for multiplying and dividing rational expressions?*

*3. How do you multiply and divide rational numbers?*

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