This is a rational equation so we run through the steps for solving rational equations. First, clear denominators. Multiply both sides by a common denominator. In this case the smallest common denominator is x(x-2).

Since the left side has two terms, we need to multiply them both.

Assemble the surviving factors

Remove parentheses.

When we combine like terms we see that we have a quadratic. Transpose all the terms to the left leaving a 0 on the right.

Now that we have a zero on one side we see if the left side factors. It does.

Set the factors equal to zero.

Let x = 4/3

Copy down the original equation

except that wherever you see an x, copy a 4/3 in parentheses.

The right simplifies when the 3's cancel, but we have more work to do on the left. In the bottom of the fraction, we have a subtraction of fraction problem, so we need common denominators.

This changes the 2 into a 6/3

or

We are now ready to invert and multiply in the compound fraction in the first term on the right.

We need common denominators on the left.

which checks.

Let x = -1.

Copy down the original equation

except that wherever you see an x, copy down a -1 in parentheses.

Do the arithmetic on the bottoms.

Find common denominators on the left.

which checks.