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Math Help - Another algebra question?

  1. #1
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    Another algebra question?

    Hello,

    Is it correct if I do this:

    vout = Vb*Ro/(Rb+Ro) - (va - vb (Ro/(Rb+Ro)) (Rf/Ra)
    vout = Vb*Ro/(Rb+Ro) - va(1 - vb (Ro/(Rb+R0)) (Rf/Ra)
    vout = Vb(Ro/(Rb+Ro)) - va(1-vb.... lost!!!!

    I need to get to:



    vout = Vb (Ro/(Rb+Ro)) (1+Ro/(Rb+Ro) -va(Rf/Ra)

    Anyone can help please!
    thank you
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  2. #2
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    Re: Another algebra question?

    Hey simplyComplex.

    Your expansion is wrong on the 2nd line: look at it and try again.
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  3. #3
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    Re: Another algebra question?

    Hi Chiro...

    Yeah I'm lookin I'm lookin!!

    vout = Vb*Ro/(Rb+Ro) - (va - vb (Ro/(Rb+Ro)) (Rf/Ra)
    vout = Vb*Ro/(Rb+Ro) - va(- vb (Ro/(Rb+Ro)) (Rf/Ra) // expanded va
    vout = Vb(Ro/(Rb+Ro) - va(-Ro/(Rb+Ro)) (Rf/Ra) // expanded vb
    and now what??

    I don't understand how the heck the answer comes to this:
    vout = Vb (Ro/(Rb+Ro)) (1+Ro/(Rb+Ro) -va(Rf/Ra)

    Thanks Chiro
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  4. #4
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    Re: Another algebra question?

    I recommend you talk to your teacher aout this because you really don't seem to understand what you are doing. You were told that your first step was wrong. Did you look at it enough to understand why it was wrong? Because, in fact, your second line here is, if anything, more wrong. In both you have attempted to factor "va" out of the second term. Okay, that uses what is technically called the "distributive property": ab+ ac= a(b+ c). That is, when you factor a term out of a sum, you have to factor it out of all terms. But the first time you did that you factored "va" out of the first term but not out of the second term. And the second time, you just ignored the first term.

    You wrote "expanded va" and "expanded vb". What do you mean by that?
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  5. #5
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    Re: Another algebra question?

    Quote Originally Posted by simplyComplex View Post
    vout = Vb*Ro/(Rb+Ro) - (va - vb (Ro/(Rb+Ro)) (Rf/Ra)

    I don't understand how the heck the answer comes to this:
    vout = Vb (Ro/(Rb+Ro)) (1+Ro/(Rb+Ro) -va(Rf/Ra)
    It doesn't. Look carefully at HallsOfIvy's post and you will see that your equation is of the form vout = (...)vb + (...) *where the (...)'s represent numbers in terms of the R's and va.

    Your "answer" is of the form vout = (...)vb. It can't be both.

    -Dan

    PS: vb and Vb are not the same variable. Math is "case sensitive."
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  6. #6
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    Re: Another algebra question?

    Hi,

    oops I think the answer I was hoping was wrong it should be:
    vout = Vb (Ro/(Rb+Ro)) (1+Rf/Ra) -va(Rf/Ra)

    So, let me start over, this is what we are starting with:

    vo = Vb*Ro/(Rb+Ro) - (va - vb (Ro/(Rb+Ro)) (Rf/Ra)

    If we take out vb we get:

    vo = Vb(Ro/(Rb+Ro)) - (va - (Ro/(Rb+Ro)) (Rf/Ra)

    If we take out va we get:

    vo = Vb(Ro/(Rb+Ro)) - va (-(Ro/(Rb+Ro)) (Rf/Ra)

    we can move the terms a little:

    vo = Vb(Ro/(Rb+Ro)) (-(Ro/(Rb+Ro)) - va (Rf/Ra)


    ****but I am supposed to get:
    vout = Vb (Ro/(Rb+Ro)) (1+Rf/Ra) -va(Rf/Ra)


    topsquart,

    It doesn't. ....
    you mean it can't come out to:

    vout = Vb (Ro/(Rb+Ro)) (1+Rf/Ra) -va(Rf/Ra)

    Let me keep trying here...

    thanks
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  7. #7
    Forum Admin topsquark's Avatar
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    Re: Another algebra question?

    Quote Originally Posted by simplyComplex View Post
    vout = Vb (Ro/(Rb+Ro)) (1+Rf/Ra) -va(Rf/Ra)
    Well, now that you fixed the parenthesis it will work.

    -Dan
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  8. #8
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    Re: Another algebra question?

    yes but, I still don't know how to get fom:
    vo = Vb(Ro/(Rb+Ro)) (-(Ro/(Rb+Ro)) - va (Rf/Ra)


    to:
    vout = Vb (Ro/(Rb+Ro)) (1+Rf/Ra) -va(Rf/Ra)


    Can someone show it step by step... I am not able to follow when math hides 4 or 5 steps to get to the last step.
    thanks
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  9. #9
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    Re: Another algebra question?

    Is vo= vout?

    Unless there is something you are not telling us, some special relation between Ro, Ra, Rb, and Rf, that's not true.
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  10. #10
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    Re: Another algebra question?

    yes its vout.

    Unless there is something you are not telling us, some special relation between Ro, Ra, Rb, and Rf, that's not true.
    I don't think so, there simple resistor values!

    vout = Vb * Ro/(Rb+Ro)-(va - vb(ro/(rb + ro))) (Rf/Ra)

    And collecting terms for va and vb, we are supposed to get to this....

    vout = Vb (Ro/(Rb+Ro)((1+Rf)/Ra) -va(Rf/Ra)

    I have been trying to see how the heck this is possible???

    thanks
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  11. #11
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    Re: Another algebra question?

    ... I finally had a little time to work at this...!!!!

    So, let me start over, this is what we are starting with:

    vo = Vb*Ro/(Rb+Ro) - (va - vb (Ro/(Rb+Ro)) (Rf/Ra)

    If we take out vb we get:

    vo = Vb(Ro/(Rb+Ro)) - (va - (Ro/(Rb+Ro)) (Rf/Ra)

    If we take out va we get:

    vo = Vb(Ro/(Rb+Ro)) - va (-(Ro/(Rb+Ro)) (Rf/Ra)


    I have been trying all morning and I can't seem to know what the next line should be?
    I am supposed to get to the following line???

    vout = Vb (Ro/(Rb+Ro)) (1+(Rf/Ra)) -va(Rf/Ra)

    How does the "1" get there? I tried over 20 different scenarios and I never get what I am supposed to get??

    Confused!
    Its 4 times I try and its four times I give up.... Help someone !
    Last edited by simplyComplex; September 10th 2013 at 07:32 AM.
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  12. #12
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    Re: Another algebra question?

    Quote Originally Posted by simplyComplex View Post
    v_o = v_b \cdot \frac{R_o}{R_b + R_o} - \left ( v_a - v_b\frac{R_o}{R_b + R_o} \right ) \cdot \frac{R_f}{R_a}
    You didn't factor the second term right. If you must factor the vb (or Vb? Math is "case sensitive!") then it must be taken out of both terms in the second term.
    v_o = v_b \left \[ \frac{R_o}{R_b + R_o} - \left ( \frac{v_a}{v_b} - \frac{R_o}{R_b + R_o} \right ) \cdot \frac{R_f}{R_a} \right \]

    I'd try this approach: Expand that second term and compare the vb term with the first term in your expression.
    v_o = v_b \cdot \frac{R_o}{R_b + R_o} - \left ( v_a - v_b\frac{R_o}{R_b + R_o} \right ) \cdot \frac{R_f}{R_a}

    v_0 = v_b \cdot \frac{R_o}{R_b + R_o} + v_b \cdot \frac{R_o}{R_b + r_o} \cdot \frac{R_f}{R_a} - v_a \cdot \frac{R_f}{R_a}

    Now factor the first two terms.

    -Dan
    Last edited by topsquark; September 10th 2013 at 09:37 AM.
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