PREVIOUS ANSWER: (7x)/(2x-5) RATIONAL EXPRESSIONS Scavengei Simplify: (18x^5y^2)/(24x^7)y^(2)

To simplify the rational expression $\frac{18x^5y^2}{24x^7y^2}$, we can follow these steps:<br /><br />1. Factor out common factors in the numerator and denominator.<br />2. Cancel out the common factors.<br /><br />Let's start by factoring out the common factors:<br /><br />$\frac{18x^5y^2}{24x^7y^2} = \frac{6 \cdot 3x^5y^2}{8 \cdot 3x^7y^2}$<br /><br />Now, we can cancel out the common factors:<br /><br />$\frac{6 \cdot 3x^5y^2}{8 \cdot 3x^7y^2} = \frac{6}{8} \cdot \frac{3x^5y^2}{3x^7y^2}$<br /><br />Simplifying further:<br /><br />$\frac{6}{8} \cdot \frac{3x^5y^2}{3x^7y^2} = \frac{3}{4} \cdot \frac{x^5y^2}{x^7y^2}$<br /><br />Finally, we can cancel out the common factors in the numerator and denominator:<br /><br />$\frac{3}{4} \cdot \frac{x^5y^2}{x^7y^2} = \frac{3}{4} \cdot \frac{1}{x^2} = \frac{3}{4x^2}$<br /><br />Therefore, the simplified form of the rational expression $\frac{18x^5y^2}{24x^7y^2}$ is $\frac{3}{4x^2}$.