Problem 8

Solve the equation

Solution

a) Multiply both sides by the common denominator :

b) Expand each term. Compute:

and

Since the second term is subtracted, it becomes

Thus, the left-hand side becomes

The right-hand side expands to

c) Form the equation:

Subtract the right-hand side from the left:

d) Divide by 3: Apply the quadratic formula:

Since , we have

Thus,

or

e) Check that and from the original denominators; both solutions are acceptable.

Answer: or