Final answer:
To find the LCD for the expressions 6/5x² and 5x/5x², we determine the LCM of the denominators. Then, we convert each expression to an equivalent expression with the denominator equal to the LCD.
Step-by-step explanation:
To find the least common denominator (LCD) for the expressions 6/5x² and 5x/5x², we need to determine the least common multiple (LCM) of the denominators. The denominators are 5x² and 5x², so the LCM is also 5x².
To convert the first expression, 6/5x², to an equivalent expression with the denominator equal to the LCD, we multiply the numerator and denominator by the factor that will make the denominator 5x². In this case, the factor is 5x²/5x².
So, 6/5x² is equivalent to (6 * 5x²)/(5x² * 5x²), which simplifies to 30x²/25x⁴.
To convert the second expression, 5x/5x², to an equivalent expression with the denominator equal to the LCD, we multiply the numerator and denominator by the factor that will make the denominator 5x². In this case, the factor is (5x²)/(5x²).
So, 5x/5x² is equivalent to (5x * 5x²)/(5x² * 5x²), which simplifies to 25x³/25x⁴.