simplify-each-complex-rational-expression-in-each-case-list-any-values-of-the-variables-for-which--5

Question

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.
$\frac{\frac{1}{6}+\frac{1}{4}}{\frac{1}{3}+\frac{1}{2}}$

Leina Wu · Accepted Answer

okay. This question were still will find this fraction on type is 1/6. Close. One home for and in the bottom is 1/3 plus 1/2. So if you want a simplified us, we can first of all, observe all the fractions and all of the denominator. We have six for three and two bullets. Identify the least a common denominator. Uh, was 643 to the least commented on merit Could be well, so I&#x27;m gonna multiply everything on top and about by positive love. So once you multiply by 12 we can&#x27;t distribute just 12 into 16 times 12. That&#x27;s gonna be too. And we have looked my one force by 12 the other three to bottom 1/3 times 12 that is for and one have times 12. That is six. We have five over time. 5/10. We can further reduced by side. You get one house. 1/2 is gonna be the simplified form of this fresh

Georgiann Andersen · Answer

you really look 12 we&#x27;re gonna simplify this and also determine what value why cannot be we have y plus one house all over to why Plus one, This is the same as saying to why plus one over two multiplying by the reciprocal to why that&#x27;s one. We can cross these out across reduction and we end up with one house. So we&#x27;ve simplified that. Now, when you look at this, the why is not going to cannot be a negative 1/2. And that being, if you set to why plus 1 to 0, you&#x27;re gonna have to y equals negative one, and why is gonna be a negative one hat? So that cannot be why?

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

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

we&#x27;re gonna simplify a complex expression. And this is number 18. And our expression is one plus one over. Why minus six over y squared. And this is all over one plus 11 over. Why? Plus 24 over y squared. First thing we need to do is simplify the numerator. So if we have one plus one over why minus six over. Why, Square, We need to get everything that has the common denominator of y squared. So we&#x27;re gonna turn the one in tow. Why? Square over y squared? Plus why? Over y squared minus six over y squared. This is gonna end up equaling y squared. Plus why minus six. All over. Why, Squirt? Now we&#x27;re gonna do the same thing. The denominator. We&#x27;re gonna simplify that one too. So we have one plus 11 over. Why? Plus 24 over. Weiss Quirk. We need to put everything over. Why Square? So it&#x27;s why squared over y squared. Plus 11. Why are 11 why? Over why plus 24 over Weiss Court. That&#x27;s gonna leave us with y squared. Plus 11. Why? Plus 24 all over. Why squared? Okay. So we can go ahead and substitute this in. So we have y squared. Plus why minus six all over. Why Square we can multiply that by the reciprocal. So we&#x27;re gonna change it Toe y squared over. Why squared? Plus 11. Why plus 24. We can cancel the y squared, and we&#x27;re gonna end up with y squared. Plus why minus six. All over. Why squared plus 11. Why? Plus 24. Now we&#x27;re gonna factor these out. Why squared? Plus, why minus six is gonna factor out to be a why, Plus three times why minus two. This is all over. Why? Plus three And why? Plus eight, we can cancel these out because there factors in both of them. That&#x27;s gonna leave us with why, minus two over Why? Plus eight. And that&#x27;s as far as you can go. So that&#x27;s your simplest form. Now, if you look at the beginning, why cannot be zero? Because that&#x27;s gonna turn those into undefined fractions. Why cannot be a naked of three, and why cannot be a negative eight

Leina Wu · 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

Problem

Simplify each complex rational expression. In eac…

Problem 7 Easy Difficulty

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.
$\frac{\frac{1}{6}+\frac{1}{4}}{\frac{1}{3}+\frac{1}{2}}$

Answer

$\frac{1}{2}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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$\frac{1}{2}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry