Simplify the following expression completely.
start fraction, x, squared, minus, 14, x, plus, 45, divided by, x, squared, minus, 18, x, plus, 81, end fraction
x
2
−18x+81
x
2
−14x+45
The expression can be factored as follows:
(x^2 - 14x + 45) / (x^2 - 18x + 81)
(x - 9)(x - 5) / (x - 9)(x - 9)
Simplifying further, we get:
(x - 5) / (x - 9)
To simplify the expression completely, we can factor the numerator and denominator and then cancel out any common factors.
The numerator is x^2 - 14x + 45, which can be factored as (x - 5)(x - 9).
The denominator is x^2 - 18x + 81, which can be factored as (x - 9)(x - 9).
Now, we can cancel out the common factor of (x - 9) from both the numerator and denominator.
The simplified expression is (x - 5)/(x - 9).
To simplify the expression, we need to factor both the numerator and the denominator and look for any common factors that can be canceled out.
Factoring the numerator:
x^2 - 14x + 45 can be factored as (x - 5)(x - 9).
Factoring the denominator:
x^2 - 18x + 81 can be factored as (x - 9)(x - 9) or simplified as (x - 9)^2.
Now, let's rewrite the expression with the factored forms of the numerator and denominator:
[(x - 5)(x - 9)] / [(x - 9)(x - 9)]
Next, we can cancel out the common factor of (x - 9) in the numerator and denominator:
(x - 5) / (x - 9)
So, the simplified expression is:
(x - 5) / (x - 9).