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

Question

Which expression is equivalent to 42 a k + 42 a k , where k &#62; 0 ?

Accepted Answer

Choice D is correct. Two fractions can be added together when they have a common denominator. Since k &#62; 0 , multiplying the second term in the given expression by k k yields 42 a k k k , which is equivalent to 42 a k 2 k . Therefore, the expression 42 a k + 42 a k can be written as 42 a k + 42 a k 2 k which is equivalent to 42 a + 42 a k 2 k . Since each term in the numerator of this expression has a factor of 42 a , the expression 42 a + 42 a k 2 k can be rewritten as 42 a 1 + 42 a k 2 k , or 42 a 1 + k 2 k , which is equivalent to &#160; 42 a ( k 2 + 1 ) k . Choice A is incorrect. This expression is equivalent to 42 a k &#160; + &#160; 42 a k . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This expression is equivalent to 42 a k &#160; + &#160; 42 a .

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