Simplify the following expression completely. (x^(2)-15 x+56)/(x^(2)+2x-63) 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 + 2x - 63. Similarly, we need to find two numbers that multiply to -63 and add up to 2. These numbers are 9 and -7. So, x^2 + 2x - 63 can be factored as (x + 9)(x - 7).Simplify Expression: Simplify the expression by canceling out the common factors. We have (x - 7)(x - 8) in the numerator and (x + 9)(x - 7) in the denominator. The common factor (x - 7) can be canceled out from both the numerator and the denominator. The simplified expression is (x - 8)/(x + 9).

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Simplify the following expression completely.

(x^(2)-15 x+56)/(x^(2)+2x-63)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}-15 x+56}{x^{2}+2 x-63}$ $\newline$ 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}+2 x-63}

\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 $x^2 + 2x - 63$ . Similarly, we need to find two numbers that multiply to $-63$ and add up to $2$ . These numbers are $9$ and $-7$ . So, $x^2 + 2x - 63$ can be factored as $(x + 9)(x - 7)$ .
Simplify Expression: Simplify the expression by canceling out the common factors. $\newline$ We have $(x - 7)(x - 8)$ in the numerator and $(x + 9)(x - 7)$ in the denominator. The common factor $(x - 7)$ can be canceled out from both the numerator and the denominator. $\newline$ The simplified expression is $\frac{x - 8}{x + 9}$ .