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Simplify. Express your answer as a single fraction in simplest form. \newline5t3+s5\frac{5t}{3} + \frac{s}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline5t3+s5\frac{5t}{3} + \frac{s}{5}
  1. Find LCM of Denominators: Find the least common multiple (LCM) of the denominators 33 and 55. The LCM of 33 and 55 is 1515 because 33 and 55 are both prime numbers and their LCM is simply their product.
  2. Make Denominators Same: Make the denominators the same by multiplying the first fraction by 55 and the second fraction by 33. This gives us (5t×5)/15+(s×3)/15(5t \times 5)/15 + (s \times 3)/15.
  3. Perform Numerator Multiplication: Perform the multiplication in the numerators. This results in (25t)/15+(3s)/15(25t)/15 + (3s)/15.
  4. Combine Fractions: Combine the fractions by adding the numerators since the denominators are the same. The combined fraction is (25t+3s)/15(25t + 3s)/15.
  5. Check for Common Factors: Check if the numerator and denominator have any common factors that can be simplified. In this case, there are no common factors between 25t+3s25t + 3s and 1515, so the fraction is already in its simplest form.

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