Simplify the following expression completely. (x^(2)+4x-5)/(x^(2)-4x-45) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. The expression is (x^(2)+4x-5)/(x^(2)-4x-45). We need to factor both the numerator and the denominator to see if there are any common factors that can be canceled out. For the numerator, we look for two numbers that multiply to -5 and add to 4. These numbers are 5 and -1. So, x^2 + 4x - 5 factors to (x + 5)(x - 1). For the denominator, we look for two numbers that multiply to -45 and add to -4. These numbers are -9 and 5. So, x^2 - 4x - 45 factors to (x - 9)(x + 5).Write Factored Form: Write the factored form of the expression. The factored form of the expression is: ((x + 5)(x - 1))/((x - 9)(x + 5))Cancel Common Factors: Cancel out the common factors. We can see that (x + 5) is a common factor in both the numerator and the denominator. We can cancel this factor out. After canceling, we get: (x - 1)/(x - 9)Write Simplified Expression: Write the simplified expression. The simplified expression is: (x - 1)/(x - 9) This is the final simplified form of the given expression.

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Simplify the following expression completely.

(x^(2)+4x-5)/(x^(2)-4x-45)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}+4 x-5}{x^{2}-4 x-45}$ $\newline$ 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-5}{x^{2}-4 x-45}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. $\newline$ The expression is $(x^{2}+4x-5)/(x^{2}-4x-45)$ . We need to factor both the numerator and the denominator to see if there are any common factors that can be canceled out. $\newline$ For the numerator, we look for two numbers that multiply to $-5$ and add to $4$ . These numbers are $5$ and $-1$ . $\newline$ So, $x^2 + 4x - 5$ factors to $(x + 5)(x - 1)$ . $\newline$ For the denominator, we look for two numbers that multiply to $-45$ and add to $-4$ . These numbers are $-9$ and $5$ . $\newline$ So, $-5$ $1$ factors to $-5$ $2$ .
Write Factored Form: Write the factored form of the expression. $\newline$ The factored form of the expression is: $\newline$ $\frac{(x + 5)(x - 1)}{(x - 9)(x + 5)}$
Cancel Common Factors: Cancel out the common factors. $\newline$ We can see that $(x + 5)$ is a common factor in both the numerator and the denominator. We can cancel this factor out. $\newline$ After canceling, we get: $\newline$ $\frac{x - 1}{x - 9}$
Write Simplified Expression: Write the simplified expression. $\newline$ The simplified expression is: $\newline$ $(x - 1)/(x - 9)$ $\newline$ This is the final simplified form of the given expression.