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Simplify each expression. In each case, list any values of the variables for which the fractions are not defined.$\left(6+\frac{12}{b}\right) \div\left(3 b-\frac{12}{b}\right)+\frac{b}{2-b}$

$-1, b \neq 0,-2,2$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 6

Complex Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

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01:41

05:34

01:46

Okay, we're going to simplify a complex expression and then identify any variables that would make it undefined. So this is a problem number 24. Our expression is six plus 12 of ruby divided by three B -12 over B plus B. Over two minus B. Yeah so the first thing we want to do is take the information in the first term and simplify that. Um in order to do that we need to have the denominator is the same. So we're going to multiply the six by B over B. So that's going to be 6b over B Plus 12 over B. We're also gonna combine or simplify the next term in order to do that. We need to get be a denominator B. So we're going to take three B times B. Which is going to be three B squared, Oliver B -12 b. 12 over B. And add B over two minus B. Okay, so we're going to end up having six B plus 12 all over B. Now when you divide, that's the same as multiplying by the reciprocal. So we're going to be over three B squared minus 12 at the B. Over 2 -7. Okay, so we can get rid of the bees And that's going to leave us with six B plus 12. All over three B squared minus 12 Plus B Over 2 -7. Okay now we're going to factor out the sixth on the new uh numerator. So we're going to make it six times B plus two on the denominator. We're going to take the three out. That's gonna leave us with B squared minus four On the 2nd 1. We're going to leave it as beyond the top but we're going to take a negative one out of there so we can make it b minus two. Okay douse or going to give the numerator the same on the denominator. We're going to go ahead and factor that B squared minus four out to be plus two and b minus two. And we can still add the B. And the negative b minus two. Okay on this first one we we can eliminate this we can eliminate the three and change this to it too. That's going to leave us with too Over B -2 -2 plus. Okay let's move the negative sign up to the top And make it be -2 on the bottom. That's gonna leave us With 2 -7. All over B -2. Mhm. Then on the top we can actually change this around so we can take the negative one And make it be -2 And put this all over B -2. We can eliminate this and our answer then is -1. To be undefined. Be cannot be zero cannot be too and it cannot be negative too

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