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Simplify. Express your answer as a single fraction in simplest form.
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Q. Simplify. Express your answer as a single fraction in simplest form.
- Identify LCD: Identify the least common denominator (LCD) for the fractions.The fractions have denominators of and . To combine these fractions, we need to find the LCD that both denominators can divide into. The LCD for and is because and both divide into it without leaving a remainder.
- Rewrite fractions: Rewrite each fraction with the LCD as the new denominator.For the first fraction, , we need to multiply the numerator and denominator by to get the LCD as the new denominator. For the second fraction, , we need to multiply the numerator and denominator by to get the LCD as the new denominator.So, we have:
- Perform multiplications: Perform the multiplications in the numerators and confirm the denominators are the same.Now that we have a common denominator, we can combine the numerators.
- Combine numerators: Combine the numerators over the common denominator.This is the expression with a single fraction.
- Check for simplification: Check if the numerator can be simplified.The terms in the numerator, and , do not have any common factors other than , and they are not like terms, so they cannot be combined or simplified further.
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