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