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After simplifying the expression, what is the numerator?[tex]\frac{x+1}{2} -\frac{x+2}{3x}[/tex]

A
−x2 + 4x + 2

B
3x2 + x − 2

C
−3x2 − 4x + 2

D
3x2 + x − 4

Respuesta :

Answer:

3x^2 +x-4

Step-by-step 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

Answer:

It's D .

Step-by-step 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).