Perform the following operation and express in simplest form. (x^(2)+9x)/(x-9)÷(x^(2)-81)/(x^(2)-7x-18) Answer:

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Perform the following operation and express in simplest form.  (x^(2)+9x)/(x-9)÷(x^(2)-81)/(x^(2)-7x-18) Answer:

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Identify and Rewrite Division: Identify the given expression and rewrite the division as multiplication by the reciprocal. The expression is (x^(2)+9x)/(x-9) ÷ (x^(2)-81)/(x^(2)-7x-18), which can be rewritten as (x^(2)+9x)/(x-9) * (x^(2)-7x-18)/(x^(2)-81).Factor Numerator and Denominator: Factor the numerator and denominator of both fractions where possible. The numerator x^(2)+9x can be factored as x(x+9). The denominator x^(2)-81 can be factored as (x+9)(x-9) because it is a difference of squares. The denominator x^(2)-7x-18 can be factored as (x-9)(x+2) because it is a quadratic expression.Rewrite with Factored Terms: Rewrite the expression with the factored terms. The expression becomes (x(x+9))/(x-9) * ((x-9)(x+2))/(x+9)(x-9).Cancel Common Factors: Cancel out common factors from the numerator and denominator. The factors (x+9) and (x-9) cancel out from the numerator and denominator. The expression simplifies to x * (x+2).Multiply Remaining Factors: Multiply the remaining factors. Multiplying x by (x+2) gives x^2 + 2x.Check for Further Simplification: Check for any further simplification. The expression x^2 + 2x cannot be factored further, so this is the simplest form.

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+9 x}{x-9} \div \frac{x^{2}-81}{x^{2}-7 x-18}$ $\newline$ Answer:

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Perform the following operation and express in simplest form.\newlinex2+9xx−9÷x2−81x2−7x−18 \frac{x^{2}+9 x}{x-9} \div \frac{x^{2}-81}{x^{2}-7 x-18} x−9x2+9x​÷x2−7x−18x2−81​\newlineAnswer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+9 x}{x-9} \div \frac{x^{2}-81}{x^{2}-7 x-18}$ $\newline$ Answer: