If the expression is written in the equivalent form what is A in terms of x?
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Choice A is correct. The form of the equation suggests performing long division on
Since the remainder 1 matches the numerator in it is clear that
A short way to find the answer is to use the structure to rewrite the numerator of the expression as recognizing the term in parentheses as a difference of squares, making the expression equal to From this, the answer is apparent. Another way to find the answer is to isolate A in the form and simplify. As with the first approach, this approach also requires students to recognize as a difference of squares that factors.
Choice B is not the correct answer. The student may have made a sign error while subtracting partial quotients in the long division.
Choice C is not the correct answer. The student may misunderstand how to work with fractions and may have tried the incorrect calculation
Choice D is not the correct answer. The student may misunderstand how to work with fractions and may have tried the incorrect calculation
Students must transform a given expression into a more useful form (from improper to proper rational form).