Simplify the following expression completely. (x^(2)+3x-10)/(x^(2)-5x+6) Answer:

Factor Numerator: First, we need to factor both the numerator and the denominator of the given expression. Factor the numerator x^2 + 3x - 10. We look for two numbers that multiply to -10 and add to 3. These numbers are 5 and -2. So, the factored form of the numerator is (x + 5)(x - 2).Factor Denominator: Now, factor the denominator x^2 - 5x + 6. We look for two numbers that multiply to 6 and add to -5. These numbers are -2 and -3. So, the factored form of the denominator is (x - 2)(x - 3).Simplify Expression: Next, we simplify the expression by canceling out the common factors in the numerator and the denominator. The common factor is (x - 2). So, the simplified form of the expression is (x + 5)/(x - 3).

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Algebra 2

Simplify variable expressions using properties

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Q. Simplify the following expression completely.

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\frac{x^{2}+3 x-10}{x^{2}-5 x+6}

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Answer:

Factor Numerator: First, we need to factor both the numerator and the denominator of the given expression. $\newline$ Factor the numerator $x^2 + 3x - 10$ . $\newline$ We look for two numbers that multiply to $-10$ and add to $3$ . These numbers are $5$ and $-2$ . $\newline$ So, the factored form of the numerator is $(x + 5)(x - 2)$ .
Factor Denominator: Now, factor the denominator $x^2 - 5x + 6$ . We look for two numbers that multiply to $6$ and add to $-5$ . These numbers are $-2$ and $-3$ . So, the factored form of the denominator is $(x - 2)(x - 3)$ .
Simplify Expression: Next, we simplify the expression by canceling out the common factors in the numerator and the denominator. $\newline$ The common factor is $(x - 2)$ . $\newline$ So, the simplified form of the expression is $\frac{x + 5}{x - 3}$ .