Simplify the expression completely if possible. (x^(2)-11 x+24)/(x^(2)-9) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator if possible. The numerator x^2 - 11x + 24 can be factored into (x - 8)(x - 3) because 8 and 3 are the numbers that multiply to 24 and add up to -11. The denominator x^2 - 9 is a difference of squares and can be factored into (x + 3)(x - 3).Write Factored Form: Write the factored form of the expression. The expression becomes ((x - 8)(x - 3))/((x + 3)(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 - 8)/(x + 3).Check Further Simplifications: Check for any further simplifications. There are no common factors left, and neither the numerator nor the denominator can be factored further. Therefore, the expression is fully simplified.

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Q. Simplify the expression completely if possible.

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\frac{x^{2}-11 x+24}{x^{2}-9}

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Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator if possible. $\newline$ The numerator $x^2 - 11x + 24$ can be factored into $(x - 8)(x - 3)$ because $8$ and $3$ are the numbers that multiply to $24$ and add up to $-11$ . $\newline$ The denominator $x^2 - 9$ is a difference of squares and can be factored into $(x + 3)(x - 3)$ .
Write Factored Form: Write the factored form of the expression. $\newline$ The expression becomes $\frac{(x - 8)(x - 3)}{(x + 3)(x - 3)}$ .
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 $\frac{x - 8}{x + 3}$ .
Check Further Simplifications: Check for any further simplifications. There are no common factors left, and neither the numerator nor the denominator can be factored further. Therefore, the expression is fully simplified.