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In $3-12,$ multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined.$$\frac{a^{2}-100}{3 a} \cdot \frac{a^{2}}{2 a-20}$$

$\frac{a^{2}+10 a}{6}, a \neq 0,10$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 3

Multiplying and Dividing Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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05:34

In $3-12,$ multiply and ex…

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In $25-30,$ perform the in…

01:43

In $13-24,$ divide and exp…

03:49

In $3-20$ , perform the in…

So for this question, were given a square minus 100 over three a times a squared over to a minus 20 and were asked to multiply these two together while also detailing what values a cannot be. In this problem, A cannot be zero or 10 as that would make thes denominators equal to zero. You can have a denominator zero. So, yeah, So before I multiply across, I'm going to factor this out as well as this denominator. And doing that would give me a minus 10 and eight plus 10. Um, it's also important to note that up here this day in one of these days will cancel out. So that means we're left with a three and the denominator here times just a a over two times a minus 10. Now, before multiply across, I can do some cross cancellation again. This a mite extended this a minus and we'll cancel each other out. And so we left with a times a question over six as our finally

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