(x^2+4x+4)/(x+2)

Jasonbradley

2 min read

·

Jun 17, 2024

16

Share

Simplifying the Expression (x^2 + 4x + 4) / (x + 2)

This expression represents a rational function, which is a fraction where both the numerator and denominator are polynomials. To simplify it, we can use the following steps:

1. Factor the Numerator

The numerator, (x^2 + 4x + 4), is a perfect square trinomial. It can be factored as:

(x + 2)(x + 2)

2. Simplify the Expression

Now we have:

(x + 2)(x + 2) / (x + 2)

Since we have (x + 2) in both the numerator and the denominator, we can cancel them out.

This leaves us with (x + 2) as the simplified expression.

Important Note:

It's crucial to remember that the simplified expression (x + 2) is only equivalent to the original expression (x^2 + 4x + 4) / (x + 2) when x ≠ -2. This is because the original expression is undefined when x = -2, as it results in division by zero.

Therefore, the final simplified form of the expression is:

(x + 2), where x ≠ -2