Simplify the following expression completely.

Question

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
​

Answer 1

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).