This is a rational equation, so we should first clear denominators. Multiply both sides by x.

We are ready to transpose. Subtract x from both sides.

Factor out the x

Divide both sides by the coefficient of the unknown.

Copy down the original equation

except that whenever you see an x, copy down the solution in parentheses.

On the top of the left, we are adding fractions. For this we need common denominators.

or

which simplifies to

If we cancel at this point, we see that it checks.