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Math Help - Changing the subject of a formula

  1. #1
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    Changing the subject of a formula

    Hello

    I'm new to this forum and I was hoping someone could please help me with something.

    I'm trying to learn algebra and am working through a book doing all the practice exercises. There is one question in particular under the subject of changing the subject of a formula that I don't know how the answer was derived.

    The question is:



    Make y the subject of Changing the subject of a formula-equation.png




    The answer is Changing the subject of a formula-equation2.png


    I can't figure out how they've come to that answer and there is no explanation in the book. Can anyone help please?

    Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Natter View Post
    Hello

    I'm new to this forum and I was hoping someone could please help me with something.

    I'm trying to learn algebra and am working through a book doing all the practice exercises. There is one question in particular under the subject of changing the subject of a formula that I don't know how the answer was derived.

    The question is:



    Make y the subject of Click image for larger version. 

Name:	equation.png 
Views:	62 
Size:	1.6 KB 
ID:	19703




    The answer is Click image for larger version. 

Name:	equation2.png 
Views:	56 
Size:	1.6 KB 
ID:	19705


    I can't figure out how they've come to that answer and there is no explanation in the book. Can anyone help please?

    Thanks
    First step is to multiply both sides by xy, the denominator of the left, to get:

    \displaystyle y + x = xy(p + q)^2

    Now how do you think you should proceed? to solve for y, you need to get y by itself on one side. you can start by getting all terms with y's in them on one side.
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  3. #3
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    Make your life easier: let k = (p+q)^2; then you have:
    (x + y) / (xy) = k
    x + y = kxy
    kxy - y = x : get it?
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  4. #4
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    Thanks everyone. No Wilmer, I don't understand that.

    Skeeter, you also sent me a reply and I have it in my email but can't see it in the actual thread anymore. I understand your rational up to the step after you subtract y from both sides. So to confirm I understand Step 1 is to multiply by xy and Step 2 is to subtract y. But then I completely don't understand the next step where 1 is subtracted. Where does the 1 come from?? Thanks all! Sorry, I probably sound really thick!!
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  5. #5
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    I've worked it out! You then factorise it which is how the 1 is obtained, and then divide by the new factorise equation. Thanks for all help!!
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  6. #6
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    Quote Originally Posted by Natter View Post
    I've worked it out! You then factorise it which is how the 1 is obtained, and then divide by the new factorise equation. Thanks for all help!!
    Correct!

    Make your life easier: let k = (p+q)^2; then you have:
    (x + y) / (xy) = k
    x + y = kxy
    kxy - y = x : get it?

    Factorize:
    y(kx - 1) = x
    Divide by kx-1:
    y = x / (kx - 1)
    Substitute back in:
    y = x / [x(p + q)^2 - 1]
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