Perform the following operation and express in simplest form. (x^(2)+4x-45)/(3x^(2))÷(x^(2)+6x-27)/(5x) Answer:

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Perform the following operation and express in simplest form.  (x^(2)+4x-45)/(3x^(2))÷(x^(2)+6x-27)/(5x) Answer:

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Factor Expressions: First, we need to factor the numerators and denominators where possible to simplify the expression. Factor (x^2 + 4x - 45) and (x^2 + 6x - 27). (x^2 + 4x - 45) can be factored into (x + 9)(x - 5). (x^2 + 6x - 27) can be factored into (x + 9)(x - 3).Rewrite with Factored Forms: Now, rewrite the original expression with the factored forms. [(x + 9)(x - 5)] / [3x^2] ÷ [(x + 9)(x - 3)] / [5x]Take Reciprocal and Multiply: Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, we will take the reciprocal of the second fraction and multiply. [(x + 9)(x - 5)] / [3x^2] * [5x] / [(x + 9)(x - 3)]Cancel Common Factors: Next, we can cancel out any common factors from the numerator and denominator. The (x + 9) terms cancel out, and we can simplify the x terms by dividing 5x by 3x^2, which leaves us with 5/3x in the numerator. [(x - 5)] / [3x] * [5] / [(x - 3)]Multiply Remaining Terms: Now, multiply the remaining terms. [(x - 5) * 5] / [3x * (x - 3)]Simplify Numerator Multiplication: Simplify the multiplication in the numerator. [5x - 25] / [3x(x - 3)]Final Simplified Form: The expression is now simplified, and we cannot simplify it further because there are no more common factors to cancel out. The final simplified form is (5x - 25) / [3x(x - 3)].

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+4 x-45}{3 x^{2}} \div \frac{x^{2}+6 x-27}{5 x}$ $\newline$ Answer:

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Perform the following operation and express in simplest form.\newlinex2+4x−453x2÷x2+6x−275x \frac{x^{2}+4 x-45}{3 x^{2}} \div \frac{x^{2}+6 x-27}{5 x} 3x2x2+4x−45​÷5xx2+6x−27​\newlineAnswer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+4 x-45}{3 x^{2}} \div \frac{x^{2}+6 x-27}{5 x}$ $\newline$ Answer: