Identify the LCD in the equation below. \( \frac{2}{x}+\frac{7}{8 x}=\frac{3}{x^{2}} \) \( 8 x \) \( x \) \( 8 x^{2} \) \( x^{2} \)
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The least common denominator (LCD) for the fractions in the equation \( \frac{2}{x}+\frac{7}{8 x}=\frac{3}{x^{2}} \) is derived from the denominators involved. The denominators are \( x \), \( 8x \), and \( x^2 \). The highest exponent of \( x \) present is \( x^2 \), and including the factor of \( 8 \) gives us \( 8x^2 \). Therefore, the LCD is \( 8x^2 \). Finding the LCD can help simplify equations and combine fractions with ease, making it crucial for solving more complex mathematical problems. Once you establish the LCD, you can multiply through by it to eliminate the fractions entirely, paving a smoother path towards finding the solution. If you're interested in diving deeper into the world of mathematics, consider engaging with resources dedicated to algebraic concepts. Websites like Khan Academy and educational YouTube channels provide great tutorials and practice exercises that make learning these concepts fun and interactive!