Why is this true? $p_x$ $x$ $(1 + {(1 - a) \over a})$ = $p_x w_x + p_y w_y$ $\Rightarrow$ $x$ = $a$ ${p_x w_x + p_y w_y } \over p_x$

Question

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 $(1 + {(1 - a) \over a})$?

$p_x$$x$ $(1 + {(1 - a) \over a})$ = $p_x w_x + p_y w_y$ $\Rightarrow$ $x$ = $a$ ${p_x w_x + p_y w_y } \over p_x$

Answer 1

Notice that $1 + {1 - a \over a}$ is simply $\frac 1 a$, therefore your equation is in fact $\frac {p_x} a x = p_x w_x + p_y w_y$, so indeed $x = a \frac {p_x w_x + p_y w_y } {p_x}.$