Question in-the
In the expression above, b and c are positive integers. If the expression is equivalent to 
and 
, which of the following could be the value of c ?
4
6
8
10
In the expression above, b and c are positive integers. If the expression is equivalent to
Hard-difficulty · SAT Math · Equivalent Expressions — Simplifying rational expressions. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice A is correct. If the given expression is equivalent to , then 
, where x isn’t equal to b. Multiplying both sides of this equation by 
yields 
. Since the right-hand side of this equation is in factored form for the difference of squares, the value of c must be a perfect square. Only choice A gives a perfect square for the value of c.
Choices B, C, and D are incorrect. None of these values of c produces a difference of squares. For example, when 6 is substituted for c in the given expression, the result is 
. The expression 
can’t be factored with integer values, and therefore isn’t equivalent to .
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