Why is this true? p x x ( 1 + ( 1 − a ) a ) = p x w x + p y w y ⇒ x = a p x w x + p y w y p x I don't see why the following equation is true - although wolfram-alpha gives me the same result, I can't figure out the steps that were made. Sure, we can simply divide the equation by p x , but what happens when we also divide ( 1 + ( 1 − a ) a )?

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Why is this true?       p    x     x   (  1  +                    (        1        −        a        )            a        ) =       p    x        w    x    +      p    y        w    y    ⇒  x =   a                    p        x                    w        x            +              p        y                    w        y                    p      x      I don&#039;t see why the following equation is true - although wolfram-alpha gives me the same result, I can&#039;t figure out the steps that were made. Sure, we can simply divide the equation by       p    x  , but what happens when we also divide   (  1  +                    (        1        −        a        )            a        )?

Norah Baxter · Accepted Answer

Notice that   1  +                    1        −        a            a       is simply       1    a  , therefore your equation is in fact             p      x        a    x  =      p    x        w    x    +      p    y        w    y  , so indeed   x  =  a                    p        x                    w        x            +              p        y                    w        y                    p      x        .

Why is this true? p x </msub> x ( 1 + <mrow class="MJX-TeXAto

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