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Divide. Write your answer in simplest form.\newline25j35j23j+2÷5j2\frac{25j^3 - 5j^2}{3j + 2} \div 5j^2

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Q. Divide. Write your answer in simplest form.\newline25j35j23j+2÷5j2\frac{25j^3 - 5j^2}{3j + 2} \div 5j^2
  1. Rewrite as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction.\newlineThe original expression is (25j35j2)/(3j+2)÷5j2(25j^3 - 5j^2)/(3j + 2) \div 5j^2. To divide by 5j25j^2, we multiply by its reciprocal, which is 1/5j21/5j^2.\newlineThe new expression is (25j35j2)/(3j+2)×1/5j2(25j^3 - 5j^2)/(3j + 2) \times 1/5j^2.
  2. Factor out common term: Factor out the common term in the numerator of the first fraction.\newlineThe numerator 25j35j225j^3 - 5j^2 can be factored to 5j2(5j1)5j^2(5j - 1).\newlineThe factored expression is (5j2(5j1))/(3j+2)×15j2(5j^2(5j - 1))/(3j + 2) \times \frac{1}{5j^2}.
  3. Cancel common terms: Cancel out the common terms in the numerator of the first fraction and the denominator of the second fraction.\newlineThe 5j25j^2 in the numerator and the 5j25j^2 in the denominator cancel each other out.\newlineThe simplified expression is (5j1)/(3j+2)(5j - 1)/(3j + 2).
  4. Check for further simplification: Check if the remaining expression can be simplified further.\newlineThe expression (5j1)/(3j+2)(5j - 1)/(3j + 2) cannot be simplified further as there are no common factors and it is not possible to factorize the terms further.

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