Simplify the expression completely if possible. (x^(2)-81)/(x^(3)+9x^(2)) Answer:

Identify Factors: Identify the common factors in the numerator and the denominator. The numerator x^2 - 81 is a difference of squares and can be factored as (x + 9)(x - 9). The denominator x^3 + 9x^2 can be factored by taking out the common factor x^2, resulting in x^2(x + 9).Factor Numerator/Denominator: Factor the numerator and the denominator. Numerator: x^2 - 81 = (x + 9)(x - 9) Denominator: x^3 + 9x^2 = x^2(x + 9)Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. The (x + 9) term is common to both the numerator and the denominator and can be canceled out. After canceling, we are left with (x - 9) in the numerator and x^2 in the denominator.Write Simplified Expression: Write down the simplified expression. The simplified expression is (x - 9)/x^2.

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Q. Simplify the expression completely if possible.

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\frac{x^{2}-81}{x^{3}+9 x^{2}}

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Answer:

Identify Factors: Identify the common factors in the numerator and the denominator. $\newline$ The numerator $x^2 - 81$ is a difference of squares and can be factored as $(x + 9)(x - 9)$ . $\newline$ The denominator $x^3 + 9x^2$ can be factored by taking out the common factor $x^2$ , resulting in $x^2(x + 9)$ .
Factor Numerator/Denominator: Factor the numerator and the denominator. $\newline$ Numerator: $x^2 - 81 = (x + 9)(x - 9)$ $\newline$ Denominator: $x^3 + 9x^2 = x^2(x + 9)$
Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. $\newline$ The $(x + 9)$ term is common to both the numerator and the denominator and can be canceled out. $\newline$ After canceling, we are left with $(x - 9)$ in the numerator and $x^2$ in the denominator.
Write Simplified Expression: Write down the simplified expression. $\newline$ The simplified expression is $(x - 9)/x^2$ .