After the fraction x plus 2 all over 2 minus the fraction x plus 1 all over 3 x have been combined using the least common denominator of 6x, what is the numerator? a. 3x2 + 4x + 1 b. 3x2 + 4x − 2 c. −3x2 − x + 4 d. −x2 + 3x + 4

(B) 3x² + 4x - 2 will be numerator of the required fraction.

Explanation: According to the question,

Given expression: (x+2)/2 - (x+1)/3x   (1)            

Since, the least common factor of 2 and 3x= 6x

So, from equation (1),  3x(x+2)/6x - 2(x+1)/6x

=(3x² + 6x - 2x - 2)/6x

= (3x² + 4x  - 2)/6x, here, 3x² + 4x  - 2 is numerator and 6x is denominator.

Thus, required answer is 3x² + 4x  - 2.