Q. Simplify. Express your answer as a single fraction in simplest form. 49p−q5
Identify LCM of Denominators: Identify the least common multiple (LCM) of the denominators 4 and q. Since 4 and q are not necessarily multiples of each other, the LCM is simply their product, which is 4q.
Rewrite with Common Denominator: Rewrite each fraction with the common denominator of 4q. To do this, multiply the numerator and denominator of the first fraction by q to get (9pq)/4q. Multiply the numerator and denominator of the second fraction by 4 to get (20)/4q.
Combine Fractions: Combine the fractions over the common denominator. This gives us (9pq−20)/4q.
Check Numerator Simplification: Check if the numerator can be simplified further. Since 9pq and 20 do not have any common factors other than 1, and we cannot simplify p since it is a variable, the numerator is already in its simplest form.
Check Fraction Simplification: Check if the fraction itself can be simplified further. Since 4q 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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