Simplify the expression completely if possible. (x^(2)+16 x+63)/(x^(2)-81) Answer:

Factorize Numerator and Denominator: Factor both the numerator and the denominator if possible. The numerator x^2 + 16x + 63 can be factored into (x + 7)(x + 9). The denominator x^2 - 81 is a difference of squares and can be factored into (x + 9)(x - 9). So, the expression becomes ((x + 7)(x + 9))/((x + 9)(x - 9)).Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. The (x + 9) term is present in both the numerator and the denominator, so they cancel each other out. The expression simplifies to (x + 7)/(x - 9).Check for Further Simplifications: Check for any further simplifications. There are no common factors left, and the expression cannot be simplified further. So, the final simplified expression is (x + 7)/(x - 9).

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Simplify the expression completely if possible.

(x^(2)+16 x+63)/(x^(2)-81)
Answer:

Simplify the expression completely if possible. $\newline$ $\frac{x^{2}+16 x+63}{x^{2}-81}$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

Full solution

Q. Simplify the expression completely if possible.

\newline

\frac{x^{2}+16 x+63}{x^{2}-81}

\newline

Answer:

Factorize Numerator and Denominator: Factor both the numerator and the denominator if possible. $\newline$ The numerator $x^2 + 16x + 63$ can be factored into $(x + 7)(x + 9)$ . $\newline$ The denominator $x^2 - 81$ is a difference of squares and can be factored into $(x + 9)(x - 9)$ . $\newline$ So, the expression becomes $\frac{(x + 7)(x + 9)}{(x + 9)(x - 9)}$ .
Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. $\newline$ The $(x + 9)$ term is present in both the numerator and the denominator, so they cancel each other out. $\newline$ The expression simplifies to $\frac{x + 7}{x - 9}$ .
Check for Further Simplifications: Check for any further simplifications. There are no common factors left, and the expression cannot be simplified further. So, the final simplified expression is $(x + 7)/(x - 9)$ .