2. Solve for x and check.

 

 

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.

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