Simplify the following expression completely. (x^(2)-x-42)/(x^(2)-12 x+35) Answer:

Factorize numerator: Factor the numerator and the denominator. The numerator x^2 - x - 42 and the denominator x^2 - 12x + 35 are both quadratic expressions that can be factored into the product of two binomials.Factorize denominator: Factor the numerator x^2 - x - 42. To factor the quadratic expression, we look for two numbers that multiply to -42 and add to -1. These numbers are -7 and 6. So, x^2 - x - 42 = (x - 7)(x + 6).Simplify expression: Factor the denominator x^2 - 12x + 35. To factor the quadratic expression, we look for two numbers that multiply to 35 and add to -12. These numbers are -5 and -7. So, x^2 - 12x + 35 = (x - 5)(x - 7).Simplify the expression by canceling out common factors. We have (x - 7)(x + 6) in the numerator and (x - 5)(x - 7) in the denominator. The common factor (x - 7) can be canceled out from both the numerator and the denominator. So, the simplified expression is (x + 6)/(x - 5).

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Simplify the following expression completely.

(x^(2)-x-42)/(x^(2)-12 x+35)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}-x-42}{x^{2}-12 x+35}$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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Q. Simplify the following expression completely.

\newline

\frac{x^{2}-x-42}{x^{2}-12 x+35}

\newline

Answer:

Factorize numerator: Factor the numerator and the denominator. $\newline$ The numerator $x^2 - x - 42$ and the denominator $x^2 - 12x + 35$ are both quadratic expressions that can be factored into the product of two binomials.
Factorize denominator: Factor the numerator $x^2 - x - 42$ . To factor the quadratic expression, we look for two numbers that multiply to $-42$ and add to $-1$ . These numbers are $-7$ and $6$ . So, $x^2 - x - 42 = (x - 7)(x + 6)$ .
Simplify expression: Factor the denominator $x^2 - 12x + 35$ . To factor the quadratic expression, we look for two numbers that multiply to $35$ and add to $-12$ . These numbers are $-5$ and $-7$ . So, $x^2 - 12x + 35 = (x - 5)(x - 7)$ .
Simplify expression: Factor the denominator $x^2 - 12x + 35$ . To factor the quadratic expression, we look for two numbers that multiply to $35$ and add to $-12$ . These numbers are $-5$ and $-7$ . So, $x^2 - 12x + 35 = (x - 5)(x - 7)$ . Simplify the expression by canceling out common factors. We have $(x - 7)(x + 6)$ in the numerator and $(x - 5)(x - 7)$ in the denominator. The common factor $(x - 7)$ can be canceled out from both the numerator and the denominator. So, the simplified expression is $(x + 6)/(x - 5)$ .