Simplify the expression completely if possible. (x^(2)-16)/(x^(2)+5x+4) Answer:

Factorize Numerator and Denominator: Factor the numerator and denominator if possible. The numerator x^2 - 16 is a difference of squares and can be factored into (x + 4)(x - 4). The denominator x^2 + 5x + 4 can be factored by finding two numbers that multiply to 4 and add to 5. These numbers are 1 and 4. So, the denominator factors into (x + 1)(x + 4).Write Expression with Factors: Write the expression with the factors. The factored form of the expression is: ((x + 4)(x - 4))/((x + 1)(x + 4))Cancel Common Factors: Cancel out the common factors. The (x + 4) term is present in both the numerator and the denominator, so they cancel each other out. This leaves us with: (x - 4)/(x + 1)Check Further Simplification: Check if further simplification is possible. The expression (x - 4)/(x + 1) cannot be simplified further as there are no common factors left.

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Simplify the expression completely if possible.

(x^(2)-16)/(x^(2)+5x+4)
Answer:

Simplify the expression completely if possible. $\newline$ $\frac{x^{2}-16}{x^{2}+5 x+4}$ $\newline$ 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}-16}{x^{2}+5 x+4}

\newline

Answer:

Factorize Numerator and Denominator: Factor the numerator and denominator if possible. $\newline$ The numerator $x^2 - 16$ is a difference of squares and can be factored into $(x + 4)(x - 4)$ . $\newline$ The denominator $x^2 + 5x + 4$ can be factored by finding two numbers that multiply to $4$ and add to $5$ . These numbers are $1$ and $4$ . $\newline$ So, the denominator factors into $(x + 1)(x + 4)$ .
Write Expression with Factors: Write the expression with the factors. $\newline$ The factored form of the expression is: $\newline$ $\frac{(x + 4)(x - 4)}{(x + 1)(x + 4)}$
Cancel Common Factors: Cancel out the common factors. $\newline$ The $(x + 4)$ term is present in both the numerator and the denominator, so they cancel each other out. $\newline$ This leaves us with: $\newline$ $\frac{x - 4}{x + 1}$
Check Further Simplification: Check if further simplification is possible. $\newline$ The expression $(x - 4)/(x + 1)$ cannot be simplified further as there are no common factors left.