SAT Mathematics Practice Test 6

Choice D is correct. Dividing $4x^2+6x$ by $4x+2$ gives:Therefore, the expression $\frac{4x^2+6x}{4x+2}$ is equivalent to $x+1-\frac{2}{4x+2}$ 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 $\frac{x(4x+2)+(4x+2)-2}{4x+2}=x+1-\frac{2}{4x+2}$Choices A and B are incorrect and may result from incorrectly factoring the numerator and denominator of the expression $\frac{4x^2+6x}{4x+2}$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.