Simplify the following expression completely. (x^(2)+4x-60)/(x^(2)-2x-24) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. The first step in simplifying a rational expression is to factor both the numerator and the denominator if possible. Let's start with the numerator x^2 + 4x - 60. We are looking for two numbers that multiply to -60 and add up to 4. These numbers are 10 and -6. So, we can factor the numerator as (x + 10)(x - 6). Now, let's factor the denominator x^2 - 2x - 24. We are looking for two numbers that multiply to -24 and add up to -2. These numbers are -6 and 4. So, we can factor the denominator as (x - 6)(x + 4).Write Factored Expression: Write the factored form of the expression. Now that we have factored both the numerator and the denominator, we can write the expression as: ((x + 10)(x - 6))/((x - 6)(x + 4))Cancel Common Factors: Cancel out the common factors. We can see that (x - 6) is a common factor in both the numerator and the denominator. We can cancel this factor out: (x + 10)/(x + 4)Check Further Simplifications: Check for any further simplifications. After canceling out the common factors, we should check if there are any further simplifications possible. In this case, there are no more common factors, and the expression cannot be simplified further. So, the simplified form of the expression is (x + 10)/(x + 4).

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Simplify the following expression completely.

(x^(2)+4x-60)/(x^(2)-2x-24)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}+4 x-60}{x^{2}-2 x-24}$ $\newline$ 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}+4 x-60}{x^{2}-2 x-24}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. $\newline$ The first step in simplifying a rational expression is to factor both the numerator and the denominator if possible. Let's start with the numerator $x^2 + 4x - 60$ . $\newline$ We are looking for two numbers that multiply to $-60$ and add up to $4$ . These numbers are $10$ and $-6$ . $\newline$ So, we can factor the numerator as $(x + 10)(x - 6)$ . $\newline$ Now, let's factor the denominator $x^2 - 2x - 24$ . $\newline$ We are looking for two numbers that multiply to $-24$ and add up to $-2$ . These numbers are $-6$ and $4$ . $\newline$ So, we can factor the denominator as $-60$ $1$ .
Write Factored Expression: Write the factored form of the expression. $\newline$ Now that we have factored both the numerator and the denominator, we can write the expression as: $\newline$ $\frac{(x + 10)(x - 6)}{(x - 6)(x + 4)}$
Cancel Common Factors: Cancel out the common factors. $\newline$ We can see that $(x - 6)$ is a common factor in both the numerator and the denominator. We can cancel this factor out: $\newline$ $(x + 10)/(x + 4)$
Check Further Simplifications: Check for any further simplifications. $\newline$ After canceling out the common factors, we should check if there are any further simplifications possible. In this case, there are no more common factors, and the expression cannot be simplified further. $\newline$ So, the simplified form of the expression is $(x + 10)/(x + 4)$ .