Simplify the expression completely if possible. (x^(2)-3x-28)/(x^(2)+6x+8) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. The given expression is (x^(2)-3x-28)/(x^(2)+6x+8). We need to factor both the numerator and the denominator to see if there are any common factors that can be canceled out.Factor Numerator: Factoring the numerator x^(2)-3x-28. We look for two numbers that multiply to -28 and add up to -3. These numbers are -7 and +4. So, x^(2)-3x-28 can be factored as (x-7)(x+4).Factor Denominator: Factoring the denominator x^(2)+6x+8. We look for two numbers that multiply to +8 and add up to +6. These numbers are +2 and +4. So, x^(2)+6x+8 can be factored as (x+2)(x+4).Simplify Expression: Simplify the expression by canceling out common factors. We have (x-7)(x+4) in the numerator and (x+2)(x+4) in the denominator. The common factor (x+4) can be canceled out from both the numerator and the denominator. The simplified expression is (x-7)/(x+2).

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Simplify the expression completely if possible.

(x^(2)-3x-28)/(x^(2)+6x+8)
Answer:

Simplify the expression completely if possible. $\newline$ $\frac{x^{2}-3 x-28}{x^{2}+6 x+8}$ $\newline$ 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}-3 x-28}{x^{2}+6 x+8}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. $\newline$ The given expression is $(x^{2}-3x-28)/(x^{2}+6x+8)$ . We need to factor both the numerator and the denominator to see if there are any common factors that can be canceled out.
Factor Numerator: Factoring the numerator $x^{2}-3x-28$ . We look for two numbers that multiply to $-28$ and add up to $-3$ . These numbers are $-7$ and $+4$ . So, $x^{2}-3x-28$ can be factored as $(x-7)(x+4)$ .
Factor Denominator: Factoring the denominator $x^{2}+6x+8$ . We look for two numbers that multiply to $+8$ and add up to $+6$ . These numbers are $+2$ and $+4$ . So, $x^{2}+6x+8$ can be factored as $(x+2)(x+4)$ .
Simplify Expression: Simplify the expression by canceling out common factors. $\newline$ We have $(x-7)(x+4)$ in the numerator and $(x+2)(x+4)$ in the denominator. The common factor $(x+4)$ can be canceled out from both the numerator and the denominator. $\newline$ The simplified expression is $\frac{x-7}{x+2}$ .