Question
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
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
Answers
There are no human answers yet.
Answered by
GPT 3.5
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).
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).
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