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Simplify. Write your answer using whole numbers and variables. \newline37qq2+4q\frac{37q}{q^2 + 4q}

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Q. Simplify. Write your answer using whole numbers and variables. \newline37qq2+4q\frac{37q}{q^2 + 4q}
  1. Simplify Term: Simplify the term 37q/q237q/q^2. To simplify a fraction, divide the numerator by the denominator. Here, we divide 37q37q by q2q^2. 37q/q2=37/q37q/q^2 = 37/q
  2. Combine Terms: Combine the simplified term with the remaining part of the expression.\newlineNow we have the simplified term 37q\frac{37}{q} and we need to add it to 4q4q.\newline37q+4q\frac{37}{q} + 4q
  3. Find Common Denominator: Find a common denominator to combine the terms.\newlineThe common denominator for the terms 37q\frac{37}{q} and 4q4q is qq. We need to express 4q4q with the common denominator qq.\newline4q=4q×(qq)=4q2q4q = 4q \times \left(\frac{q}{q}\right) = \frac{4q^2}{q}
  4. Combine Over Common Denominator: Combine the terms over the common denominator.\newlineNow we can combine the terms over the common denominator qq.\newline37+4q2q\frac{37 + 4q^2}{q}
  5. Check for Further Simplification: Check if the expression can be simplified further. The expression (37+4q2)/q(37 + 4q^2)/q is already in its simplest form. There are no common factors that can be canceled out.

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