Which of the following is equivalent to `(4x^2 + 6x)/(4x+2)` ?

Options

A. x
B. x+4
C. `x-2/(4x+2)`
D. `x+1 - 2/(4x+2)`

Answer

D

Explanation

Dividing `4x^2+6x` by 4x+2 gives :
Therefore , the expression `(4x^2+6x)/(4x+2)` is equivalent to `x+1 - 2/(4x+2)` .
Alternate approach: The numerator of the given expression, `4x^2 + 6x`, can be rewritten in terms of the denominator, 4x + 2, as follows: `4x^2 + 2x + 4x + 2 − 2`, or x(4x + 2) + (4x + 2) − 2. So the given expression can be rewritten as
`(x(4x+2)+(4x+2)-2)/(4x+2)=x+1 - 2/(4x+2)`
Choices A and B are incorrect and may result from incorrectly factoring the numerator and
denominator of the expression `(4x^2 + 6x)/(4x+2)` and then incorrectly identifying common factors in the two factored expressions. Choice C is incorrect and may result from a variety of mistakes made when performing long division.