Simplify the expression completely if possible. (x^(2)-2x-15)/(x^(2)-9) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator if possible. The numerator is a quadratic expression that can be factored into two binomials. The denominator is a difference of squares which can also be factored. Let's factor the numerator: x^2 - 2x - 15. We are looking for two numbers that multiply to -15 and add up to -2. These numbers are -5 and +3. So, x^2 - 2x - 15 = (x - 5)(x + 3). Now let's factor the denominator: x^2 - 9. This is a difference of squares and can be factored into (x + 3)(x - 3). The expression now looks like this: (x - 5)(x + 3) / (x + 3)(x - 3).Factor Quadratic Expressions: Cancel out the common factors. We have (x + 3) in both the numerator and the denominator, so we can cancel them out. The expression simplifies to: (x - 5) / (x - 3).Cancel Common Factors: Check for any further simplification. There are no common factors left in the numerator and the denominator, and neither the numerator nor the denominator can be factored further. Therefore, the expression is fully simplified.

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Simplify the expression completely if possible.

(x^(2)-2x-15)/(x^(2)-9)
Answer:

Simplify the expression completely if possible. $\newline$ $\frac{x^{2}-2 x-15}{x^{2}-9}$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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Q. Simplify the expression completely if possible.

\newline

\frac{x^{2}-2 x-15}{x^{2}-9}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator if possible. $\newline$ The numerator is a quadratic expression that can be factored into two binomials. The denominator is a difference of squares which can also be factored. $\newline$ Let's factor the numerator: $x^2 - 2x - 15$ . $\newline$ We are looking for two numbers that multiply to $-15$ and add up to $-2$ . These numbers are $-5$ and $+3$ . $\newline$ So, $x^2 - 2x - 15 = (x - 5)(x + 3)$ . $\newline$ Now let's factor the denominator: $x^2 - 9$ . $\newline$ This is a difference of squares and can be factored into $(x + 3)(x - 3)$ . $\newline$ The expression now looks like this: $\newline$ $(x - 5)(x + 3) / (x + 3)(x - 3)$ .
Factor Quadratic Expressions: Cancel out the common factors. $\newline$ We have $(x + 3)$ in both the numerator and the denominator, so we can cancel them out. $\newline$ The expression simplifies to: $\newline$ $(x - 5) / (x - 3)$ .
Cancel Common Factors: Check for any further simplification. $\newline$ There are no common factors left in the numerator and the denominator, and neither the numerator nor the denominator can be factored further. $\newline$ Therefore, the expression is fully simplified.