Which expression is equivalent to 42a ⁄ k + 42ak, where k 0 ?

Question

Which expression is equivalent to 42a ⁄ k + 42ak, where k > 0 ?

Accepted Answer

Choice D is correct. Two fractions can be added together when they have a common denominator. Since k > 0, multiplying the second term in the given expression by k ⁄ k yields (42ak)k ⁄ k , which is equivalent to 42ak 2 ⁄ k . Therefore, the expression 42a ⁄ k + 42ak can be written as 42a ⁄ k + 42ak 2 ⁄ k , which is equivalent to 42a + 42ak 2 ⁄ k . Since each term in the numerator of this expression has a factor of 42a, the expression 42a + 42ak 2 ⁄ k can be rewritten as 42a(1) + 42a(k 2 ) ⁄ k , or 42a(1 + k 2 ) ⁄ k , which is equivalent to 42a(k 2 + 1) ⁄ k . Choice A is incorrect. This expression is equivalent to 42a ⁄ k + 42a ⁄ k . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This expression is equivalent to 42a ⁄ k + 42a.

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