Question

Question is below

A. x + 2
B. x + 3
C. x - 2
D. x + 1

Answer 1

D. x + 1

Explanation:

The expression
`(x^2+3x+2)/(x+2)` can be simplified as follows:

`x^2 + 3x + 2`

Doing middle term factorisation

`= x^2+(2+1)x+2`

`=x^2+2x+1x+2`

`=(x + 2)(x + 1)`

Again

Dividing both side by x+2.

`(x^2 + 3x + 2)/(x + 2) = ((x + 2)(x + 1))/(x + 2)`

we get

`(x^2 + 3x + 2)/(x + 2)= x + 1`

Therefore, the expression

`(x^2+3x+2)/(x+2)` is equivalent to D. x + 1.

Note that the expression is only equivalent to x + 1 when x is not equal to -2. If x = -2, then the expression is undefined.