Final answer:
The question from a high school mathematics class involves simplifying an algebraic expression using common denominators and possibly applying the quadratic formula if simplification does not yield factored terms.
Step-by-step explanation:
The question involves the simplification of a complex algebraic expression. It requires factoring and possibly using the quadratic formula to solve for the variable x. When encountering a problem where the denominator is the same in both fractions, one strategy is to combine the numerators over the common denominator and then simplify the resulting expression if possible. In cases where a perfect square is seen on both sides of the equation or when the equation can be written as a perfect square, taking the square root of both sides may simplify the solving process drastically.
To solve for x, you may need to rearrange the expression into standard quadratic form ax² + bx + c = 0, and then apply the quadratic formula if factoring is not suitable. Finally, evaluate the numeric solutions for x, considering both the positive and negative results provided by the quadratic formula.