Simplify the following expression completely. (x^(2)+15 x+56)/(x^(2)+3x-28) Answer:

Factor Numerator: Factor the numerator x^2 + 15x + 56. To factor the quadratic expression, we need to find two numbers that multiply to 56 and add up to 15. These numbers are 7 and 8. So, x^2 + 15x + 56 can be factored as (x + 7)(x + 8).Factor Denominator: Factor the denominator x^2 + 3x - 28. Similarly, we need to find 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).Simplify Expression: Simplify the expression by canceling out the common factors. The factored form of the expression is ((x + 7)(x + 8))/((x + 7)(x - 4)). We can cancel out the common factor (x + 7) from the numerator and the denominator. The simplified expression is (x + 8)/(x - 4).

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Simplify the following expression completely.

(x^(2)+15 x+56)/(x^(2)+3x-28)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}+15 x+56}{x^{2}+3 x-28}$ $\newline$ Answer:

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Algebra 2

Simplify rational expressions

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Q. Simplify the following expression completely.

\newline

\frac{x^{2}+15 x+56}{x^{2}+3 x-28}

\newline

Answer:

Factor Numerator: Factor the numerator $x^2 + 15x + 56$ . To factor the quadratic expression, we need to find two numbers that multiply to $56$ and add up to $15$ . These numbers are $7$ and $8$ . So, $x^2 + 15x + 56$ can be factored as $(x + 7)(x + 8)$ .
Factor Denominator: Factor the denominator $x^2 + 3x - 28$ . Similarly, we need to find 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 $(x + 7)(x - 4)$ .
Simplify Expression: Simplify the expression by canceling out the common factors. $\newline$ The factored form of the expression is $\frac{(x + 7)(x + 8)}{(x + 7)(x - 4)}$ . $\newline$ We can cancel out the common factor $(x + 7)$ from the numerator and the denominator. $\newline$ The simplified expression is $\frac{x + 8}{x - 4}$ .