Which of the following statements are true of the equation (2x^2 + 5x + 2) / (2x + 4)?

Question

I. The domain is x ≠ 2 
II. (2x^2 + 5x + 2) / (2x + 4) = x + .5 for any real number 
III. (2x^2 + 5x + 2) / (2x + 4) is equivalent to x + .5

Answer 1

The rational expression (2x² + 5x + 2)/(2x + 4)

Simplify the rational expression.

Now factorize the numerator 2x² + 5x + 2

= 2x² + 4x + x + 2

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

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

(2x² + 5x + 2)/(2x + 4) = [(x + 2)(2x + 1)]/2(x + 2)

= (2x + 1)/2

= (2x/2) + (1/2)

= x + 0.5

(2x² + 5x + 2)/(2x + 4) is equivalent to x + 0.5 for any real number.

(2x² + 5x + 2)/(2x + 4) is equivalent to x + 0.5.

Option ii and iii are correct.