Q. Simplify. Express your answer as a single fraction in simplest form. 54p+5pq2
Identify common denominator: Identify the common denominator for the fractions54p and 5pq2. Since both denominators already have a common factor of 5, the least common denominator (LCD) is 5pq.
Adjust fractions: Adjust the fractions so that they both have the common denominator of 5pq. The first fraction, 54p, needs to be multiplied by qq to have the denominator 5pq. The second fraction, 5pq2, already has the common denominator.
Multiply numerator and denominator: Multiply the numerator and denominator of the first fraction by q to get the common denominator. This gives us (4p⋅q)/(5⋅q) which simplifies to 5pq4pq.
Combine fractions: Combine the fractions now that they have the same denominator. This gives us (4pq+2)/5pq.
Check for further simplification: Check if the resulting fraction can be simplified further. Since 4pq and 2 do not have any common factors other than 1, and the denominator 5pq cannot be simplified with the numerator, the fraction is already in its simplest form.
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