First clear denominators. The smallest common denominator is
Q(x - a), so multiply both sides by Q(x - a).
The parentheses on the left tell us that we must multiply both
of the terms by Q(x - a)
This will get rid of all the denominators. Assemble the
surviving factors.
Remove parentheses
and we see that we can subtract a Qa from both sides. Transpose the
Pa to the other side of the equation.
and divide both sides by the coefficient of the unknown.
Check. Copy down the original equation
except that wherever you see an x, copy down the solution in
parentheses.
In the bottom of the first term on the left, we are subtracting
fractions, so we need common denominators.
After we put the fractions in the bottom of the first term on the left
over a common denominator and subtract, we see that the term
simplifies to
We are now ready to invert and multiply
Factor out an a and cancel
This simplifies to
Amazingly we have common denominators.
or
and it checks.