$ a \frac{b}{d} + bz = c\frac{b}{d} N $
$ N + \frac{b}{d} + z = A $
I am trying to solve this for z , but i seem to get a very large and messy answer when it should be
$ z = \frac{c}{ c+d} ( A - \frac{b}{d} -\frac{a}{c} )$
can someone show me how to get this ? thank you
you can get your "final answer" by doing the following:
From the second equation:
$$ z= A-N-\frac{b}{d} $$
Rewrite N in the first equation as:
$$ N = \frac{a}{c}+\frac{zd}{c} $$
Substitute:
$$ z= A-N-\frac{b}{d} = A - \left(\frac{a}{c}+\frac{zd}{c}\right) - \frac{b}{d} $$
Doing some algebra and simplifying you can get:
$$ z+\frac{zd}{c} = A-\frac{a}{c}-\frac{b}{d} $$
or
$$ z\left(1+\frac{d}{c}\right) = A-\frac{a}{c}-\frac{b}{d} $$
Can you proceed from here?