800/(200 + x) = 640/(200-x)

Multiply both sides by (200+x)(200-x) also called removing the denominators. Step by step,

First multiply by (200+x) both sides

800 (200+x) / (200+x) = 640 (200+x)/(200-x)

800 = 640 (200+x)/(200-x)

Now multiply by (200-x) both sides

800(200-x) = 640(200+x)(200-x)/(200-x)

800(200-x) = 640(200+x)

Now expand and group, then solve. This is exactly what happens when you have

a/b = c/d and multiply both sides by bd to result in ad = bc