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Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{1+\frac{3}{b}+\frac{2}{b^{2}}}{1-\frac{1}{b^{2}}}$

$\frac{b+2}{b-1}, b \neq 0,-1,1$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 6

Complex Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Campbell University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

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01:32

In mathematics, the absolu…

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01:46

Simplify each complex rati…

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Okay, This question. We are simplifying a complex, rational expressions the one plus three over B plus two over the square divide by one liners, one over b squared. In order for us to simplify this expression, we need to take care of these denominator B B Square and A B squared. So we need to multiply everything by a common denominator common dominator, apparently by B and B Square. We can tell the common the least. A common denominator would be be square. So let's multiply everything by three squares when one plus three would be plus two over the square times the square on the bottom. We have one Mina's one over B squared times speaker, but let's distribute the B square to all the terms inside of the open pregnancies. So the first multiplication we've got us be square 2nd 3 Overbey times be square that IHS the Read Be and then to over the score times be square the beast. Where would be reduced? We get to but the bottom one time speed square. We have B squared now one of the B squared times be square and that's one. Keep going. We can factor the top. The new murder could be factored as B plus two times B plus one. In terms of the denominator, confected eyes will be plus one times B minus one. So if the requirements of match we can, we can divide both the top and bottom by B plus one. We get B plus two over B minus one. So this is the simplified form. The simplified form can be done. Okay, when the requirement of this rational expression are satisfied. Which means if you see a denominator, 11 is one of would be squared is cannot do zero. There are, like other denominator, as be square cannot be zero and b cannot be zero. Well, let's see, in the 1st 1 we have won over Bay Square cannot be won, which means B squared cannot be one of the one. So being squared cannot be won. You cannot be plus or minus what we're just a square root of what the second and third requirement tell us. Being cannot be zero. So in journal, if you look at the beast, our beat cannot be zero cannot e plus minus one. And then the simplified form of this expression will be B plus two over B minus one

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