Perform the following operation and express in simplest form. (x+5)/(x^(2)+4x-5)÷(9x+9)/(x^(2)-1) Answer:

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Perform the following operation and express in simplest form.  (x+5)/(x^(2)+4x-5)÷(9x+9)/(x^(2)-1) Answer:

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Factor Denominators: First, we need to factor the denominators of both fractions to simplify the expression. The denominator of the first fraction is x^2 + 4x - 5, which factors into (x + 5)(x - 1). The denominator of the second fraction is x^2 - 1, which is a difference of squares and factors into (x + 1)(x - 1).Rewrite as Multiplication: Next, we will rewrite the division of the two fractions as a multiplication by the reciprocal of the second fraction. (x+5)/(x^2+4x-5) ÷ (9x+9)/(x^2-1) becomes (x+5)/((x+5)(x-1)) * (x^2-1)/(9x+9).Simplify by Canceling: Now, we can simplify the expression by canceling out common factors. The (x+5) in the numerator of the first fraction cancels with the (x+5) in its denominator. The (x^2-1) in the numerator of the second fraction is (x+1)(x-1), and the (9x+9) in its denominator can be factored as 9(x+1).Final Simplified Expression: After canceling the common factors, we are left with: 1/(x-1) * (x-1)/(9(x+1)). The (x-1) in the numerator and denominator cancel each other out.The final simplified expression is: 1/(9(x+1)).

Perform the following operation and express in simplest form. $\newline$ $\frac{x+5}{x^{2}+4 x-5} \div \frac{9 x+9}{x^{2}-1}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{x+5}{x^{2}+4 x-5} \div \frac{9 x+9}{x^{2}-1}$ $\newline$ Answer: