Define variable. Show work

3/8 = 7/x+1

I assume you mean 3/8 = 7/(x+1).

Multiply both sides by x+1.

3/8x + 3/8 = 7

Subtract 3/8 from both sides.

3/8x = 6 5/8 = 53/8

Multiply both sides by 8/3.

x = 53/8 * 8/3 = ?