Find the stationary points of the function f(x,y) = xy subject to the
constraint 1/x + 1/y = 1, and find the value for f at these points.
So far I have,

$$f(x,y) = xy$$$$g(x,y) = {1 \over x} + {1 \over y} -1$$
$$H = f(x,y) - \lambda[g(x,y)]$$$$H = xy - {\lambda \over x} - {\lambda \over y} + \lambda $$
$${\delta H \over \delta x} = {y +{ \lambda \over x^2}} = 0$$$${\delta H \over \delta y} = {x +{ \lambda \over y^2}} = 0$$$${\delta H \over \delta \lambda} = 1 - {1 \over x} - {1 \over y} = 0$$

I've managed to get values for the variables but I can only obtain them in terms dependant

Question

Find the stationary points of the function f(x,y) = xy subject to the 
constraint 1/x + 1/y = 1, and find the value for f at these points.
So far I have,

$$f(x,y) = xy$$$$g(x,y) = {1 \over x} + {1 \over y} -1$$
$$H = f(x,y) - \lambda[g(x,y)]$$$$H = xy - {\lambda \over x} - {\lambda \over y} + \lambda $$
$${\delta H \over \delta x} = {y +{ \lambda \over x^2}} = 0$$$${\delta H \over \delta y} = {x +{ \lambda \over y^2}} = 0$$$${\delta H \over \delta \lambda} = 1 - {1 \over x} - {1 \over y} = 0$$

I've managed to get values for the variables but I can only obtain them in terms dependant