Simplify the expression completely if possible.
start fraction, x, squared, plus, 16, x, plus, 63, divided by, x, squared, minus, 81, end fraction
x
2
−81
x
2
+16x+63
The expression cannot be simplified any further.
To simplify the expression (x^2 + 16x + 63) / (x^2 - 81), we can look for any common factors that can be canceled out.
First, let's factor the numerator and denominator:
Numerator: x^2 + 16x + 63 can be factored as (x + 9)(x + 7).
Denominator: x^2 - 81 can be factored as (x + 9)(x - 9).
Now we can cancel out the common factors:
[(x + 9)(x + 7)] / [(x + 9)(x - 9)].
Since (x + 9) is common to both the numerator and denominator, we can cancel it out:
(x + 7) / (x - 9).
Therefore, the simplified expression is (x + 7) / (x - 9).
To simplify the expression, we first need to factor both the numerator and the denominator.
The numerator, x^2 + 16x + 63, can be factored as (x + 7)(x + 9).
The denominator, x^2 - 81, is a difference of squares and can be factored as (x + 9)(x - 9).
Now that we have factored the expression, we can cancel out the common factors in the numerator and denominator. In this case, both (x + 9) terms cancel each other out.
So the simplified expression is:
(x + 7) / (x - 9)