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.