Simplify the following expression completely.
start fraction, x, squared, plus, x, minus, 6, divided by, x, squared, minus, 4, x, minus, 21, end fraction
x
2
−4x−21
x
2
+x−6
To simplify the expression completely, we need to factor the numerator and the denominator.
The numerator is x^2 + x - 6. This can be factored as (x + 3)(x - 2).
The denominator is x^2 - 4x - 21. This can be factored as (x + 3)(x - 7).
Now we can rewrite the expression as:
(x^2 + x - 6) / (x^2 - 4x - 21)
= (x + 3)(x - 2) / (x + 3)(x - 7)
We can cancel out the common factor of (x + 3) in the numerator and denominator.
= (x - 2) / (x - 7)
So, the simplified expression is (x - 2) / (x - 7).
To simplify the given expression completely, we need to factor both the numerator and the denominator, and then cancel out any common factors.
Let's start by factoring the numerator and the denominator separately.
Numerator: x^2 + x - 6
This expression can be factored as (x - 2)(x + 3).
Denominator: x^2 - 4x - 21
This expression can be factored as (x - 7)(x + 3).
Now, let's substitute the factored forms into the original expression:
(x^2 + x - 6) / (x^2 - 4x - 21)
Substituting the factored forms, we get:
((x - 2)(x + 3)) / ((x - 7)(x + 3))
Now, we can cancel out the common factor of (x + 3):
(x - 2) / (x - 7)
So, the simplified form of the expression is (x - 2) / (x - 7).
To simplify the expression completely, we need to factor the numerator and the denominator.
The numerator can be factored as:
x^2 + x - 6 = (x + 3)(x - 2)
The denominator can be factored as:
x^2 - 4x - 21 = (x - 7)(x + 3)
Now, we can rewrite the expression as:
[(x + 3)(x - 2)] / [(x - 7)(x + 3)]
Notice that (x + 3) appears in both the numerator and the denominator. We can cancel out these common factors:
= (x - 2) / (x - 7)
Therefore, the simplified expression is (x - 2)/(x - 7).