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Math Help - Rational Expressions- NEED HELP PLZ

  1. #1
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    Rational Expressions- NEED HELP PLZ

    Hi guys
    We were to simplify these equations but im not sure im doing it right. Could someone (all steps shown please) help me with these???

    Equation 1: 5t^4 - 10^2
    /(divided by)
    t^5 - 4t

    Equation 2: 15t^4
    /(divided by)
    10t^5 + 25t^3

    Please if you could show me how to do this id be really greatful
    <3 Sarah
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    Quote Originally Posted by SaRah<3 View Post
    Hi guys
    We were to simplify these equations but im not sure im doing it right. Could someone (all steps shown please) help me with these???

    Equation 1: 5t^4 - 10^2
    /(divided by)
    t^5 - 4t

    Equation 2: 15t^4
    /(divided by)
    10t^5 + 25t^3

    Please if you could show me how to do this id be really greatful
    <3 Sarah

    Well you dont really have equations, you have expressions, you need to have an = sign for it to be an equation. But anyway, here goes.

    1. (5t^4 - 10t^2)/(t^5 - 4t)
    we cant really do much with this one, just factor a t from the top and bottom (did you learn factorization?).

    so we get t(5t^3 - 10t)/t(t^4 - 4) = (5t^3 - 10t)/(t^4 - 4) since the t's cancel.

    2. 15t^4/(10t^5 + 25t^3)
    we can factor 5's out of the top and bottom, as well as t^3. so we get:

    5t^3(3t)/5t^3(2t^2 + 5)

    the 5t^3 cancels from the top and bottom leaving:

    3t/(2t^2 + 5)

    Are you sure there was no equal sign for these? If there is any step that ou dont understand, or if you dont understand how to factorize just tell me, i will explain simpler
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    Thank you so much for responding, I was worried no one would respond.
    There were no equal signs in the "expressions" so I understand that they aren't equations (my bad :P).
    I don't really understand how you got what you did for the first one, but you are right considering I know very little of how to do this.
    I will look at it closer and try to figure it out. But thank you so much for your help. Your the greatest
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    Quote Originally Posted by SaRah<3 View Post
    Thank you so much for responding, I was worried no one would respond.
    There were no equal signs in the "expressions" so I understand that they aren't equations (my bad :P).
    I don't really understand how you got what you did for the first one, but you are right considering I know very little of how to do this.
    I will look at it closer and try to figure it out. But thank you so much for your help. Your the greatest
    I need you to tell me exactly what you dont get. If you are completely lost, you can tell me also, and i'll just redo it trying to explain every step
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SaRah<3 View Post
    Thank you so much for responding, I was worried no one would respond.
    There were no equal signs in the "expressions" so I understand that they aren't equations (my bad :P).
    I don't really understand how you got what you did for the first one, but you are right considering I know very little of how to do this.
    I will look at it closer and try to figure it out. But thank you so much for your help. Your the greatest
    Hmm, i expected yo to have more trouble with the second one, since the factorization was a bit more ambitious. But any way, here is the explanation for 1. Remember, when we want to simplify something, we want to break it down, either by canceling two things if we have a rational function (that's just a fancy name for saying we have something divided by something), or adding and subtracting things so that we end up with an expression that is simpler than the one we started with. Usually that means fewer terms, but it can also mean redusing powers and minimizing constants.

    now to 1. We had (5t^4 - 10t^2)/(t^5 - 4t). Now we examine the function to see if we have anything common to the numerator (the top) and the denomenator (the bottom). Let's first consider the top. Looking at 5t^4 - 10t^2, what can you see that is common to both terms? well, the t's should jump out at you first. we have t's in 5t^4 and in 10t^2. When we factorize, we take out the lower powers of the variables, so we would take out a common t^2 from 5t^4 and 10t^2, to get something like t^2(5t^2 - 10). However, we are evaluating the entire function to see what will cancel. since we cannot get t^2 out of each term at the bottom, we will not take out t^2, but only t. Notice that what is left of the 5t^4 is 5t^3, this is becuase when we multiply like bases, we add the powers. Therefore, i want to make sure that if i undo what i just did, i could get back the original power. so t*t^3 = t^(1+3) = t^4. ok? Now, what else do we see common? well, 5 is common to both the remaining 5t^3 and 10t, but we will not take these out. why not? well, we are evaluating the entire function to see what can cancel, and when we look at the bottom, there is no 5 common among the terms at the bottom, so taking a 5 out would be meaningless. We can get t out of the bottom. and end up with t(t^4 - 4), and there is nothing else common among the terms, besides 1, but it would not make sense taking out 1. So now we have a t on the outside of both functions on the top and bottom, so we can cancel them and end up with
    (5t^3 - 10t)/(t^4 - 4)
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    Aww tanks so much for the explanation. You really didnt have to do that.

    Along with the expressions we were suppose to graph using the reduced expression. I'm using a calculator while doing this....so I'm thinking that is my main problem.

    For both expressions we were to find out the x and y variable from 0 to 6 (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6)

    I keep getting all different answers....I took a scan of the worksheet showing the answers I got....does it look right to you??
    Thanks in advance please and thank-you

    http://img247.imageshack.us/img247/3980/scannr3.jpg
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    Quote Originally Posted by SaRah<3 View Post
    Aww tanks so much for the explanation. You really didnt have to do that.

    Along with the expressions we were suppose to graph using the reduced expression. I'm using a calculator while doing this....so I'm thinking that is my main problem.

    For both expressions we were to find out the x and y variable from 0 to 6 (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6)

    I keep getting all different answers....I took a scan of the worksheet showing the answers I got....does it look right to you??
    Thanks in advance please and thank-you

    http://img247.imageshack.us/img247/3980/scannr3.jpg

    Sorry Sarah, but i have to be heading to a class now, and i wont be out of class until 5 pm this evening. Hopefully someone else can help you if you have to have it done before then. 5 wont work, it'll have to be after 7. And by the way, at first glance, your value for Cb when t=0 is wrong, it should be 0
    Last edited by Jhevon; March 1st 2007 at 02:52 PM.
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    Quote Originally Posted by SaRah<3 View Post
    Aww tanks so much for the explanation. You really didnt have to do that.

    Along with the expressions we were suppose to graph using the reduced expression. I'm using a calculator while doing this....so I'm thinking that is my main problem.

    For both expressions we were to find out the x and y variable from 0 to 6 (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6)

    I keep getting all different answers....I took a scan of the worksheet showing the answers I got....does it look right to you??
    Thanks in advance please and thank-you

    http://img247.imageshack.us/img247/3980/scannr3.jpg
    Here are the answers to your table (see the next reply):

    I typed the formulas into Excel and evaluated them because I couldn't bother doing them all. I will show you how to calculate 1 for Ca and one for Cb
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  9. #9
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    Quote Originally Posted by SaRah<3 View Post
    Aww tanks so much for the explanation. You really didnt have to do that.

    Along with the expressions we were suppose to graph using the reduced expression. I'm using a calculator while doing this....so I'm thinking that is my main problem.

    For both expressions we were to find out the x and y variable from 0 to 6 (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6)

    I keep getting all different answers....I took a scan of the worksheet showing the answers I got....does it look right to you??
    Thanks in advance please and thank-you

    http://img247.imageshack.us/img247/3980/scannr3.jpg
    Here it is, i hope. Ok, so you need excel to open it. Tell me if you have a problem opening it, I'm waiting...
    Attached Files Attached Files
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  10. #10
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    Thankyou so much for your help. I know I asked way too much of you!
    But your help is greatly appericiated
    I opened it fine and I undertstand how you got the answers you did. I typed it in wrong in the calculator -_-;;;
    lol But THANK-YOU SOOOOOO MUCH
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