simplify-each-complex-rational-expression-in-each-case-list-any-values-of-the-variables-for-which-15

Question

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

Leina Wu · Accepted Answer

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&#x27;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&#x27;s one over B squared times speaker, but let&#x27;s distribute the B square to all the terms inside of the open pregnancies. So the first multiplication we&#x27;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&#x27;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&#x27;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&#x27;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

Georgiann Andersen · Answer

Okay, We&#x27;re gonna do problem Number 10. We have a B minus one over B. Oh, over one of her P minus one. Let&#x27;s simplify the top, and we&#x27;re gonna make that be square minus one all over B and the bottom one, it&#x27;s gonna be one over one minus be all over the So we&#x27;re gonna have B squared minus one all over B. And we&#x27;re gonna multiply that by the reciprocal. Both the denominator, which is e over one minus B beacon cress, reduced bees. That&#x27;s gonna leave us with B squared minus one all over one, minus E. Factoring out the numerator, we&#x27;re gonna have a B minus one plus one. Bottom one. Let&#x27;s take out a negative one. We&#x27;re gonna end up making this B minus one. So now we can cross. We can get rid of the B minus one. Leaving us would be less one all over a negative one, which this Samos saying naked of a B plus one RV cannot be zero. And it cannot bay one

Leina Wu · Answer

locating this question. We have a complex, rational expression. Three letters, three over big survived by B minus one. So let&#x27;s simplify this fracture. In order to take care of this, be over here. We can multiply the top and the bottom of this fraction by a common denominator, which is gonna be B in this case. So I&#x27;m gonna multiply both your top and bottom by the beat. And once you do this, we can distribute to be to the open from seats. So in the top, we have three B minus three. Uh, in the bottom, we can keep it as B minus one times feet on the top. We noticed that there is three and a three, so we can factor out the three B minus one. And the bottom is B minus one time speak. So when the requirements are met, we have we can cancel. The beeman is one on the top of bottom. What&#x27;s simply divide B minus 13 over. Be ask to simplify before the reality Is that simplify For now, let&#x27;s see. What is the requirement on the beat on the B? In the very beginning, we should cut the original expression. Three. Overbey divide by being minus one. So notice that beam on is one is in the denominator. So be money is one cannot be zero being animal denominator. Also, there&#x27;s a three months be three over. Be so be cannot be zero. But tell us b can to B one from the first inequality and B can&#x27;t be zero in a second. Inequality in general you will be can be any value but zero and one. And for those values, um, for any other values, you&#x27;re complex fraction complex, rational expression can be simplified as three over the

Georgiann Andersen · Answer

Okay, We&#x27;re gonna look at problem 14. We have one over to X. That&#x27;s one over three X Oh, over one of her X Square. Let&#x27;s simplify the numerator. We&#x27;ve got one over to X plus one over three X. In order to simplify this, we need to have the denominator the same so we can take to x times the three X and we can take the 1st 1 and take that times the three x and add the two X That&#x27;s gonna leave us with Ivax over six X Square. We can move that back in and make this five x over six X squared. We&#x27;re gonna buy it all that by one over X squared. That&#x27;s the same as saying five x over six x squared. I&#x27;m so reciprocal X squared over one. It could cross reduce the X squared, and that leaves us with five acts over six. So that&#x27;s our answer right there. That&#x27;s our simplified answer. Now they want to know what values cannot be Us. You look at the top originally all of us denominators. If any one of them would turn out to be a zero, um, that would make this and undefined so ex cannot be zero

Georgiann Andersen · Answer

Hey, we&#x27;re gonna solve her problem, mate. We have one less one over a all over a plus one. If we make this into basically I&#x27;m mixed number. That&#x27;s the same s a plus one all over a And this is all being divided by a plus one. This is the same as saying a plus one all over, eh? We&#x27;re gonna multiply by the reciprocal. So that&#x27;s one over. A less one we can cross reduce. That&#x27;s a plus one goes an A plus one, multiply one times one and get one multiple a multiple, a buy one and you get Hey, so that&#x27;s our answer here. Now, the variables that cannot be are zero because in the very top numerator, we have won over a And if that day would be zero that be undefined and you wouldn&#x27;t be able to add the one and the other one is negative on because on the original denominator a plus one If you set out to zero your ace gonna be zero r a will be negative one

Leina Wu · Answer

okay. In his question, we&#x27;re simplifying a fraction to minus two over D over one over D minus one. So when we&#x27;re simplified this weekend, tickle cats, the fractions aimed this conference fraction here to over the e and one day and notice that they all have the d e in the denominator so we can multiply by the common denominator d both on top and bottom. And once we divest, we can to simplify this too. Um, distribute the state we have to de Mona&#x27;s to other D Time state the vibe I won over d Times Day minus one times. So by distributing the d to the open pregnancies, then we have to de monies to end of all right one minus two. Not noticed that the to t minus two on the top you can factor after two. So I&#x27;m gonna fact out to Steve. Miner is one in the bottom. You have one. Run the state and for the demon is one in a woman s t. I can write. The demon is one as negative one times one line. It&#x27;s deep just by flipping the order. But tonight by one ministate, one minus t. When the status on when the requirement is that it&#x27;s fired. This woman is we could be reduced. So we get negative to asked a simplifies dancer. But when we&#x27;re doing this, we haven&#x27;t pay attention to when this would be a ballot. So for De de cannot be a certain value, not just look at this original extraction to over prior to Manistee over one over T minus one. So we know that he is in in the bottom, so he cannot be zero. And for this woman isn&#x27;t demon is one. It&#x27;s in the denominator of distractions. A woman is d minus one cannot be zero, which tell us one Mona&#x27;s de cannot be won and do you cannot be won. So with these two information in mind, we know D cannot be zero and positive. That&#x27;s synthesis. The problem

Problem

Simplify each complex rational expression. In eac…

Problem 17 Hard Difficulty

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

Answer

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

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Anna Marie V.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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

Algebra 2 and Trigonometry

Anna Marie V.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Caleb E.

Kristen K.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry