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Simplify. Express your answer as a single fraction in simplest form. \newline9p4−5q\frac{9p}{4} - \frac{5}{q}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline9p4−5q\frac{9p}{4} - \frac{5}{q}
  1. Identify LCM of Denominators: Identify the least common multiple (LCM) of the denominators 44 and qq. Since 44 and qq are not necessarily multiples of each other, the LCM is simply their product, which is 4q4q.
  2. Rewrite with Common Denominator: Rewrite each fraction with the common denominator of 4q4q. To do this, multiply the numerator and denominator of the first fraction by qq to get (9pq)/4q(9pq)/4q. Multiply the numerator and denominator of the second fraction by 44 to get (20)/4q(20)/4q.
  3. Combine Fractions: Combine the fractions over the common denominator. This gives us (9pq−20)/4q(9pq - 20)/4q.
  4. Check Numerator Simplification: Check if the numerator can be simplified further. Since 9pq9pq and 2020 do not have any common factors other than 11, and we cannot simplify pp since it is a variable, the numerator is already in its simplest form.
  5. Check Fraction Simplification: Check if the fraction itself can be simplified further. Since 4q4q is the least common multiple we found and there are no common factors between the numerator and the denominator, the fraction is already in its simplest form.

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