Simplify algebra expression

How would you simplify the following equation to x = something?

1/x = 1/y + b

x*1/x= x(1/y+ b) Multiply both sides by x
x/x= x(1/y+ b) Simplify
1 = x(1/y+ b)
1/(1/y+ b)=x(1/y+ b)/(1/y+ b) Divide each side by (1/y + b)
1/(1/y+ b)= x Simplify
x =1/(1/y+ b) put x on the left for simplicities sake.

How would you simplify the following equation to x = something?

1/x = 1/y + b
= 1/y + by/y
= ( 1+by) y
so x/1 = y / ( 1+by)
x = y / (1+by)

1. Multiply by x on both sides. 1 = (1/y + b)x
2. divide by (1/y + b) on both sides. 1 / (1/y+b) = x

1/x = (1/y) + b = (1 + by) / y

Now just flip both sides over:
x = y / (1 + by)

1/x = 1/y + b
x = y + b