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Simplify. Express your answer as a single fraction in simplest form. \newline5t+37t\frac{5}{t} + \frac{3}{7t}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline5t+37t\frac{5}{t} + \frac{3}{7t}
  1. Identify LCM of denominators: Identify the least common multiple (LCM) of the denominators tt and 7t7t. Since tt is a factor of 7t7t, the LCM is 7t7t.
  2. Rewrite fractions with LCM: Rewrite each fraction with the LCM as the denominator. To do this, multiply the numerator and denominator of the first fraction by 77 to get the common denominator of 7t7t. This gives us (5×7)/(t×7)+3/7t(5\times7)/(t\times7) + 3/7t, which simplifies to 35/7t+3/7t35/7t + 3/7t.
  3. Add fractions with common denominator: Add the fractions now that they have the same denominator. The sum is (35+3)/7t(35 + 3)/7t.
  4. Simplify numerator by adding: Simplify the numerator by adding the numbers. This gives us 387t.\frac{38}{7t}.
  5. Check for further simplification: Check if the fraction can be simplified further. Since 3838 and 77 have no common factors other than 11, the fraction is already in its simplest form.

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