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Simplify. Express your answer as a single fraction in simplest form. \newline9a5+ab2\frac{9a}{5} + \frac{ab}{2}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline9a5+ab2\frac{9a}{5} + \frac{ab}{2}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators 55 and 22. The LCM is 1010.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by 22 and the second fraction by 55. This gives us 9a×210+ab×510\frac{9a \times 2}{10} + \frac{ab \times 5}{10}.
  3. Perform multiplication for numerators: Perform the multiplication for both numerators. This results in (18a)/10+(5ab)/10(18a)/10 + (5ab)/10.
  4. Combine fractions: Combine the fractions since the denominators are the same. The combined fraction is (18a+5ab)/10(18a + 5ab)/10.
  5. Check for further simplification: Check if the numerator can be simplified further. Since there is no common factor between 18a18a and 5ab5ab other than 'aa', we cannot simplify the expression further.

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