Q. Simplify. Express your answer as a single fraction in simplest form. w53−3v3w2
Identify LCD: Identify the least common denominator (LCD) for the two fractions.The LCD for the fractions w53 and 3v3w2 is 3v3w5 because it is the smallest expression that both denominators can divide into without leaving a remainder.
Rewrite with common denominator: Rewrite each fraction with the common denominator.For the first fraction, multiply both the numerator and the denominator by w53v3w5, which simplifies to 3v3.For the second fraction, multiply both the numerator and the denominator by 3v3w3v3w5, which simplifies to w4.The new fractions are 3v3w53×3v3 and 3v3w52×w4.
Perform multiplications: Perform the multiplications for each fraction.The first fraction becomes (9v3)/(3v3w5).The second fraction becomes (2w4)/(3v3w5).
Combine fractions: Combine the fractions over the common denominator.Now that both fractions have the same denominator, we can combine them into a single fraction:(9v3)/(3v3w5)−(2w4)/(3v3w5)=(9v3−2w4)/(3v3w5).
Simplify expression: Simplify the expression if possible.In this case, there are no common factors in the numerator that can be canceled with the denominator. Therefore, the expression is already in its simplest form.
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