Question

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

Answer 1

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

Step-by-step 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.

Answer 2

Let's work out the process to find the numerator:
(x+2)/2 - (x+1)/3x Factor using the LCD, 6x
3x(x+2)/6x - 2(x+1)/6x
(3x² + 6x - 2x - 2)/6x
= (3x² + 4x - 2)/6x

Answer is B) 3x² + 4x - 2