Question

Which expression is equivalent to the expression

Answer 1

The trick with these is to just try a number.  c=1

( (6+3)/(-4+2) ) / ( (2+1)/(4-2) ) = (9/-2)/(3/2)) = -3

Last choice.

If there was a none of the above we'd have to do the algebra, which is straightforward:

$\dfrac{ \frac{6c^2+3c}{-4c+2} } { \frac{2c + 1}{4c - 2} }=\dfrac{6c^2+3c}{-4c+2} \cdot \dfrac{4c - 2}{2c + 1}$

$=\dfrac{4c-2}{-4c+2}\cdot\dfrac{6c^2+3c}{2c + 1}$

$=(-1)\cdot\dfrac{3c(2c+1)}{2c + 1}$

$=-3c$

Answer 2

This simplifies to -3c, with the constraint that c should not be equal to 1/2.