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Multiply. Write your answer in simplest form. $\newline$ $\frac{j + 1}{j^2} \times (j + 5)$

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Multiply and divide rational expressions

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Q. Multiply. Write your answer in simplest form.

\newline

\frac{j + 1}{j^2} \times (j + 5)

Distribute Terms: Distribute $(j + 5)$ across the terms in the numerator $(j + \frac{1}{j^2})$ . We will apply the distributive property $a(b + c) = ab + ac$ . $(j + \frac{1}{j^2}) * (j + 5) = j(j + 5) + (\frac{1}{j^2})(j + 5)$
Apply Distributive Property: Multiply each term in the parentheses by $j$ and $1/j^2$ respectively. $\newline$ $j(j) + j(5) + (1/j^2)(j) + (1/j^2)(5)$ $\newline$ This simplifies to: $\newline$ $j^2 + 5j + 1/j + 5/j^2$
Multiply Terms: Combine like terms if possible. $\newline$ In this case, there are no like terms to combine, so the expression remains as is. $\newline$ $j^2 + 5j + \frac{1}{j} + \frac{5}{j^2}$
Combine Like Terms: Write the answer in the simplest form. $\newline$ Since there are no common factors to cancel out or combine, the expression is already in its simplest form. $\newline$ $j^2 + 5j + \frac{1}{j} + \frac{5}{j^2}$

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