Solving a system of equations?

Equation 1:

x[(1/z) + 1] - y(1/z) - 1/z = y     

Equation 2:

y[(1/z) + z] - x(1/z) = -x     

becomes:     

y = [-z + 1]/[z(z^2 + 2z +1)]     

Hint: Express equation 2 in terms of x and plug into equation 1.

1. 

My attempt at isolating x in equation

2: 

y[(1/z) + z] - x(1/z) = -x   

y[(1/z) + z] = -x + x(1/z)   

y[(1/z) + z] = x[ -1 + (1/z)]   

y[(1/z) + z] = x[(1/z) - 1]   

y[(1/z) + z]/[(1/z) - 1] = x  

Equation 2: y[(1/z) + z] - x(1/z) = -x  <<<  use the 'hint' ... solve fr x

  y[(1/z) + z] =  -x + x(1/z)

x[(1/z) - 1]  =  y[(1/z) + z]

   x = y[(1/z) + z] / [(1/z) - 1]

  =====  now plug into eq 1

  Equation 1: x[(1/z) + 1] - y(1/z) - 1/z = y

   y[(1/z) + z] / [(1/z) - 1][(1/z) + 1] - y(1/z) - 1/z = y

  ...  from here do a lot of algebra steps t solve for y

 It is just algebra .. I leave the rest for you

So, start by applying their hint. Isolating x in the 2nd eqs gives x = ?

Answer that & we will proceed. 

OK. Now just plug it into the 1st eqs to get

y[(1/z) + z] / [(1/z) - 1][(1/z) + 1] - y(1/z) - 1/z = y

Now, just work at it to get it to the desired form.

Start by isolating y. A little more simplification leads to the desired form.