Perform the following operation and express in simplest form. (x+1)/(4x-20)÷(x^(2)-1)/(x^(2)+x-2) Answer:

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Perform the following operation and express in simplest form.  (x+1)/(4x-20)÷(x^(2)-1)/(x^(2)+x-2) Answer:

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Simplify Expression: First, we need to simplify the expression by changing the division to multiplication by the reciprocal of the second fraction. (x+1)/(4x-20) ÷ (x^2-1)/(x^2+x-2) = (x+1)/(4x-20) * (x^2+x-2)/(x^2-1)Factor Polynomials: Next, we factor each polynomial if possible. The first denominator 4x-20 can be factored out as 4(x-5). The second numerator x^2+x-2 can be factored into (x+2)(x-1). The second denominator x^2-1 is a difference of squares and can be factored into (x+1)(x-1). So, we rewrite the expression with factored terms: (x+1)/(4(x-5)) * ((x+2)(x-1))/((x+1)(x-1))Cancel Common Factors: Now, we cancel out the common factors in the numerator and the denominator. The (x+1) in the first numerator and the second denominator cancel out, as do the (x-1) in the second numerator and denominator. This leaves us with: 1/4 * (x+2)/(x-5)Multiply Remaining Terms: Finally, we multiply the remaining terms. (1/4) * (x+2)/(x-5) = (x+2)/(4(x-5)) This is the expression in its simplest form.

Perform the following operation and express in simplest form. $\newline$ $\frac{x+1}{4 x-20} \div \frac{x^{2}-1}{x^{2}+x-2}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{x+1}{4 x-20} \div \frac{x^{2}-1}{x^{2}+x-2}$ $\newline$ Answer: