X+8
____
x2 + 11x +24
factor the denominator (x+8)(x+3)
then reduce by dividing out the common fractions.
Sure, let's dive into the math clownery!
So, we have the expression (x+8) divided by (x^2 + 11x + 24), which can be factored as (x+8)(x+3). Well, well, well... It seems like we have a common factor of (x+8) in both the numerator and the denominator. It's a classic case of "divorce-iate" the fractions!
Let's use our clownish powers of division and reduce this expression by dividing out the common factor. It's like untangling a clown wig – except in this case, we're untangling fractions.
(x+8) / (x^2 + 11x + 24) = (x+8) / [(x+8)(x+3)]
Now, let's wave our magical clown wand and see what happens next. Oh, look! We have a common (x+8) in the numerator and the denominator. So, they cancel each other out, leaving us with...
= 1 / (x+3)
Tada! We've successfully divided out the common fractions. We went from a clown car packed with (x+8) and (x+3) to just (x+3) sitting cool and alone in the driver's seat.
To reduce the fraction, we need to divide both the numerator and denominator by the greatest common factor (GCF). In this case, the GCF is (x + 8).
Let's divide the numerator (X + 8) by (x + 8):
(X + 8)/(x + 8) = 1
Now, let's divide the denominator (x^2 + 11x + 24) by (x + 8):
(x^2 + 11x + 24)/(x + 8) = (x + 3)
Therefore, the reduced fraction is:
1/(x + 3)
To factor the denominator of the fraction x+8 / x^2 + 11x + 24, we need to find two binomials that, when multiplied together, give us the quadratic expression.
We can start by looking for two numbers whose sum is equal to the coefficient of x (which is 11) and whose product is equal to the constant term (which is 24). In this case, the numbers that meet these criteria are 3 and 8.
Therefore, we can rewrite the quadratic expression as (x+3)(x+8). Now our fraction becomes:
(x+8) / (x+3)(x+8)
To reduce the expression, we can divide out the common factor, which is (x+8), from the numerator and denominator.
So, the final simplified expression is:
1 / (x+3)