solve for x
(1/x) + (1/y) = z
i multiplied by xy to get rid of the denominators:
y + x = zxy
then
x = zxy -y
from here i have no idea.....
As a general rule, at least 2 equations are required to solve 2 variables. At least 3 equations are required to solve 3 variables.
So unless you left out some other information, it is not possible to find a unique solution. The question most likely wants you to find x in terms of the other 2 variables, which you did well. From here, move the zxy over to the left and factorise x out.
$\displaystyle \frac{1}{x} + \frac{1}{y} = z$
$\displaystyle \frac{1}{x} = z - \frac{1}{y}$
$\displaystyle x = \frac{1}{z - \frac{1}{y}}$
$\displaystyle x = \frac{1}{\frac{yz}{y} - \frac{1}{y}}$
$\displaystyle x = \frac{1}{\frac{yz - 1}{y}}$
$\displaystyle x = \frac{y}{yz - 1}$.