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Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.$\frac{8 a b-4 b^{2}}{6 a b}$

$\frac{4 a-2 b}{3 a}$$a, b \neq 0$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 2

Simplifying Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

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In mathematics, the absolu…

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Write each rational expres…

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Okay, so we're going to reduce this rational expression as well as list the values of the variables where this rational expression will be undefined. So we start with the undefined part because we want to do that before we reduce things. And so we look at the denominator and win the denominator when either A or B zero, this will be undefined. Because when we multiply any number by zero here, that's going to be zero and zero. And the denominator means on defied. So if a a zero or be a zero than this will, this expression here will be undefined. So now let's get to reducing. So whenever we add or subtract in the numerator and we just have only multiplication in the denominator, we just separate this out so we'll have eight a. Be divided by 6 80 minus four b squared over six a. B. So here, when I have these a B and a B, those are going to cancel out and you see that we have common factors here. So we have a common factor of two, so I'll have divide top and bottom by two. I get four in the numerator and three in the denominator and then also trapped here and again. We have common factor of two. So this will become a two. This will become a three. The A stays as is, and we lose this be. And we only have one left up top here. Right? So it's a B squared, which you could also write as b squared minus one, because that's the rules of exponents. And so then you're left with just a B because two minus one is one in the numerator, so I have to be in the numerator and a three a and the denominator.

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