SAT Mathematics Practice Test 6

Choice D is correct. Dividing $4{\mathit{x}}^2+6\mathit{x}$ by $4\mathit{x}+2$ gives:
Therefore, the expression $\frac{4{\mathit{x}}^2+6\mathit{x}}{4\mathit{x}+2}$ is equivalent to $\mathit{x}+1-\frac{2}{4\mathit{x}+2}$ Alternate approach: The numerator of the given expression,$4{\mathit{x}}^2+6\mathit{x},$ can be rewritten in terms of the denominator,$4\mathit{x}+2$, as follows: $4{\mathit{x}}^2+2\mathit{x}+4\mathit{x}+2-2$, or $\mathit{x}\left(4\mathit{x}+2\right)+\left(4\mathit{x}+2\right)-2.$ So the given expression can be rewritten as $\frac{\mathit{x}\left(4\mathit{x}+2\right)+\left(4\mathit{x}+2\right)-2}{4\mathit{x}+2}=\mathit{x}+1-\frac{2}{4\mathit{x}+2}$
Choices A and B are incorrect and may result from incorrectly factoring the numerator and denominator of the expression $\frac{4{\mathit{x}}^2+6\mathit{x}}{4\mathit{x}+2}$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.