%2F(x%2B3).jpeg "(x^2+6x+9)/(x+3)")
Simplifying the Expression (x^2 + 6x + 9) / (x + 3)
This expression can be simplified by factoring the numerator and then canceling common factors.
Factoring the Numerator
The numerator, x² + 6x + 9, is a perfect square trinomial. It can be factored as:
(x + 3)(x + 3)
Cancelling Common Factors
Now we have:
(x + 3)(x + 3) / (x + 3)
Since (x + 3) appears in both the numerator and denominator, we can cancel them out. This leaves us with:
x + 3
Restrictions
It's important to note that the original expression is undefined when x = -3. This is because the denominator becomes zero, which is not allowed in division.
Therefore, the simplified expression (x + 3) is equivalent to the original expression for all values of x except x = -3.
Conclusion
By factoring the numerator and canceling common factors, we simplified the expression (x² + 6x + 9) / (x + 3) to x + 3, with the restriction that x ≠ -3.