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    Hi,

    I am struggling to rearrange the equation for A_1=\dfrac{B_1}{1-B_2} into B_1=\dfrac{A_1}{1+A_2}. I also have the information that A_2=\dfrac{B_2}{1-B_2} which I know how to translate into B_2=\dfrac{A_2}{1+A_2}. Could someone please show me how to do this. Thanks.
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    Well, take   B_2=\dfrac{A_2}{1+A_2} and substitute into A_1=\dfrac{B_1}{1-B_2} to give A_1=\dfrac{B_1}{1-\dfrac{A_2}{1+A_2}}.

    Now multiply by the denominator and rearrange:
    B_1=A_1-\dfrac{A_1A_2}{1+A_2}=\dfrac{A_1  (1+A_2)}{1+A_2}-\dfrac{A_1A_2}{1+A_2}=\dfrac{A_1  +A_1A_2-A_1A_2}{1+A_2}=\dfrac{A_1}{1+A_2  }.
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    (Original post by kfkle)
    Well, take   B_2=\dfrac{A_2}{1+A_2} and substitute into A_1=\dfrac{B_1}{1-B_2} to give A_1=\dfrac{B_1}{1-\dfrac{A_2}{1+A_2}}.

    Now multiply by the denominator and rearrange:
    B_1=A_1-\dfrac{A_1A_2}{1+A_2}=\dfrac{A_1  (1+A_2)}{1+A_2}-\dfrac{A_1A_2}{1+A_2}=\dfrac{A_1  +A_1A_2-A_1A_2}{1+A_2}=\dfrac{A_1}{1+A_2  }.
    This is the gift that keeps on giving. Thanks for your input, Sonny Jim. You've just saved my bacon. <3
 
 
 
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Updated: April 22, 2011
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