Question

After simplifying the expression, what is the numerator?
`(x+1)/(2) -(x+2)/(3x)`

A
−x2 + 4x + 2

B
3x2 + x − 2

C
−3x2 − 4x + 2

D
3x2 + x − 4

Answer 1

It's D .

Explanation:

The Lowest Common Denominator of 2 and 3x is 6x.

So we multiply each fraction by 6x. This gives us:

6x ( x + 1) / 2 - 6x( x + 2) / 3x

= 3x(x + 1) - 2(x + 2)

= 3x^2 + 3x - 2x - 4

= 3x^2 + x - 4 = the numerator (answer).

Answer 2

3x^2 +x-4

Explanation:

x+1 x+2

------- - -----------

2 3x

The common denominator is 6x so multiply the first term by 3x/3x and the second term by 2/2

x+1 3x x+2 2

-------* ---- - -----------*-----

2 3x 3x 2

3x^2+3x 2x+4

----------------- - -----------

6x 6x

Combine terms

3x^2 +3x -2x-4

------------------------

6x

3x^2 +x-4

------------------------

6x