Which expression is equivalent to 4 4 x - 5 - 1 x + 1 ?

Question

Accepted Answer

Choice D is correct. The expression 4 4 x - 5 - 1 x + 1 can be rewritten as 4 4 x - 5 + - 1 x + 1 . To add the two terms of this expression, the terms can be rewritten with a common denominator. Since x + 1 x + 1 = 1 , the expression 4 4 x - 5 can be rewritten as x + 1 4 x + 1 4 x - 5 . Since 4 x - 5 4 x - 5 = 1 , the expression - 1 x + 1 can be rewritten as 4 x - 5 - 1 4 x - 5 x + 1 . Therefore, the expression 4 4 x - 5 + - 1 x + 1 can be rewritten as x + 1 4 x + 1 4 x - 5 + 4 x - 5 - 1 4 x - 5 x + 1 , which is equivalent to x + 1 4 + 4 x - 5 - 1 x + 1 4 x - 5 . Applying the distributive property to each term of the numerator yields 4 x + 4 + - 4 x + 5 x + 1 4 x - 5 , or 4 x + - 4 x + 4 + 5 x + 1 4 x - 5 . Adding like terms in the numerator yields 9 x + 1 4 x - 5 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Question 16d897