%2F(x%2B5).jpeg "(x^2+8x+15)/(x+5)")
Simplifying the Rational Expression (x^2 + 8x + 15) / (x + 5)
This article will walk through simplifying the rational expression (x^2 + 8x + 15) / (x + 5).
Factoring the Numerator
The first step is to factor the numerator, x^2 + 8x + 15. We are looking for two numbers that add up to 8 and multiply to 15. These numbers are 3 and 5.
Therefore, we can factor the numerator as (x + 3)(x + 5).
Simplifying the Expression
Now we have the expression:
[(x + 3)(x + 5)] / (x + 5)
Since we have (x + 5) 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 = -5 because it would result in division by zero. Therefore, the simplified expression, x + 3, is valid for all values of x except x = -5.
Conclusion
We have successfully simplified the rational expression (x^2 + 8x + 15) / (x + 5) to x + 3, with the restriction that x cannot equal -5. This process involves factoring the numerator and canceling out common factors.