QuestionMay 5, 2026

Simplify the following expression completely. (x^2-14x+45)/(x^2)-18x+81

Simplify the following expression completely. (x^2-14x+45)/(x^2)-18x+81
Simplify the following expression
completely.
(x^2-14x+45)/(x^2)-18x+81

Solution
4.3(242 votes)

Answer

\frac{x - 5}{x - 9} Explanation 1. Factor the numerator x^2 - 14x + 45 factors as (x - 9)(x - 5) because -9 and -5 multiply to 45 and sum to -14. 2. Factor the denominator x^2 - 18x + 81 factors as (x - 9)(x - 9) since -9 and -9 multiply to 81 and sum to -18. 3. Simplify the fraction Cancel one (x - 9) from numerator and denominator, leaving \frac{x - 5}{x - 9}.

Explanation

1. Factor the numerator <br /> $x^2 - 14x + 45$ factors as $(x - 9)(x - 5)$ because $-9$ and $-5$ multiply to $45$ and sum to $-14$. <br /><br />2. Factor the denominator <br /> $x^2 - 18x + 81$ factors as $(x - 9)(x - 9)$ since $-9$ and $-9$ multiply to $81$ and sum to $-18$. <br /><br />3. Simplify the fraction <br /> Cancel one $(x - 9)$ from numerator and denominator, leaving $\frac{x - 5}{x - 9}$.
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