Starting equation: 1
w
+ 1
y
= 1
x
Avoid hastily writing "w + y = x": try w=y=2 and x=1
Instead, first multiply both sides by (w y x):
(w y x) 1
w
+ (w y x) 1
y
= (w y x) 1
x
y x + w x = w y

Re-write the left side using a(b+c)=ab+ac:
x(y + w) = w y

Finally, divide both sides by (y + w):
x(y + w)
(y + w)
=  w y 
y + w

x =  w y 
y + w