Simplify the following expression completely. (x^(2)-13 x+30)/(x^(2)-12 x+27) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. The numerator x^2 - 13x + 30 can be factored into (x - 10)(x - 3) because 10 and 3 are the numbers that multiply to 30 and add up to -13. The denominator x^2 - 12x + 27 can be factored into (x - 9)(x - 3) because 9 and 3 are the numbers that multiply to 27 and add up to -12.Rewrite with Factored Forms: Rewrite the expression with the factored forms. The expression becomes ((x - 10)(x - 3))/((x - 9)(x - 3)).Cancel Common Factors: Cancel out the common factors. The (x - 3) term is present in both the numerator and the denominator, so they cancel each other out. The expression simplifies to (x - 10)/(x - 9).Check for Further Simplifications: Check for any further simplifications. There are no further simplifications possible, and there are no common factors left. The expression is now in its simplest form.

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Q. Simplify the following expression completely.

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\frac{x^{2}-13 x+30}{x^{2}-12 x+27}

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Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. $\newline$ The numerator $x^2 - 13x + 30$ can be factored into $(x - 10)(x - 3)$ because $10$ and $3$ are the numbers that multiply to $30$ and add up to $-13$ . $\newline$ The denominator $x^2 - 12x + 27$ can be factored into $(x - 9)(x - 3)$ because $9$ and $3$ are the numbers that multiply to $(x - 10)(x - 3)$ $0$ and add up to $(x - 10)(x - 3)$ $1$ .
Rewrite with Factored Forms: Rewrite the expression with the factored forms. $\newline$ The expression becomes $\frac{(x - 10)(x - 3)}{(x - 9)(x - 3)}$ .
Cancel Common Factors: Cancel out the common factors. $\newline$ The $(x - 3)$ term is present in both the numerator and the denominator, so they cancel each other out. $\newline$ The expression simplifies to $\frac{x - 10}{x - 9}$ .
Check for Further Simplifications: Check for any further simplifications. There are no further simplifications possible, and there are no common factors left. The expression is now in its simplest form.