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  1. #1
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    help

    i need help on solving problems like this one
    (z+4/z+5)=(z+4/z+1)+1
    solve for z
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  2. #2
    MHF Contributor
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    Quote Originally Posted by DaProphet View Post
    i need help on solving problems like this one
    (z+4/z+5)=(z+4/z+1)+1
    solve for z
    Do you mean this?

     <br />
\frac{z+4}{z+5}\;=\;\frac{z+4}{z+1}+1<br />

    That is NOT what you have written.

    Can you do anything with this part?

     <br />
\frac{z+4}{z+1}+1<br />

    Perhaps \frac{z+4}{z+1}+\frac{z+1}{z+1}?

    How did I get that? Does that make any difference?
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  3. #3
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    the way that you wrote it out is the way that i was trying to write it out like
    and im not cure about the second part
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  4. #4
    Senior Member pacman's Avatar
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    ,

    Solving for z, you may multiply both sides with (z + 5)(z + 1), we get

    (z + 4)(z + 1) = (z + 4)(z + 5) + (z + 5)(z + 1),

    z^2 + 5z + 4 = z^2 +9z + 20 + z^2 + 6z + 5, rearranging

    0 = (z^2 + z^2 - z^2) + (9z + 6z - 5z) + (20 + 5 - 4)

    0 = z^2 + 10z + 21, factoring

    0 = (z + 7)(z + 3),

    thus, z = -3 and -7

    I have plotted it below, see . . . .
    Attached Thumbnails Attached Thumbnails help-z.gif  
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  5. #5
    Senior Member pacman's Avatar
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    this is a much better plot, the intersections are the values of z that solves the equation


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