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

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Powers of a power: variable bases

Full solution

Q. Simplify. Write your answer using whole numbers and variables.

\newline

\frac{37q}{q^2 + 4q}

Simplify Term: Simplify the term $37q/q^2$ . To simplify a fraction, divide the numerator by the denominator. Here, we divide $37q$ by $q^2$ . $37q/q^2 = 37/q$
Combine Terms: Combine the simplified term with the remaining part of the expression. $\newline$ Now we have the simplified term $\frac{37}{q}$ and we need to add it to $4q$ . $\newline$ $\frac{37}{q} + 4q$
Find Common Denominator: Find a common denominator to combine the terms. $\newline$ The common denominator for the terms $\frac{37}{q}$ and $4q$ is $q$ . We need to express $4q$ with the common denominator $q$ . $\newline$ $4q = 4q \times \left(\frac{q}{q}\right) = \frac{4q^2}{q}$
Combine Over Common Denominator: Combine the terms over the common denominator. $\newline$ Now we can combine the terms over the common denominator $q$ . $\newline$ $\frac{37 + 4q^2}{q}$
Check for Further Simplification: Check if the expression can be simplified further. The expression $(37 + 4q^2)/q$ is already in its simplest form. There are no common factors that can be canceled out.

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