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Multiply. Write your answer in simplest form. $\newline$ $\frac{s}{s + 1} \times \frac{4s - 5}{1}$

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Multiply and divide rational expressions

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Q. Multiply. Write your answer in simplest form.

\newline

\frac{s}{s + 1} \times \frac{4s - 5}{1}

Identify Terms: Identify the terms to be multiplied and set up the multiplication. $\newline$ We have the fraction $\frac{s}{s + 1}$ and the expression $(4s - 5)$ . To multiply these, we simply multiply the numerators and keep the denominators as is, since the second expression is not a fraction.
Multiply Numerators: Multiply the numerators. $\newline$ The numerator of the first fraction is $s$ , and the entire second expression $(4s - 5)$ is treated as the numerator of a fraction with a denominator of $1$ . So we multiply $s$ by $(4s - 5)$ . $\newline$ $s \times (4s - 5) = 4s^2 - 5s$
Write Product: Write the product as a single fraction. $\newline$ Since the denominator of the first fraction is $(s + 1)$ and the second expression is over $1$ , the product of the two is $(4s^2 - 5s)$ over $(s + 1)$ . $\newline$ $(4s^2 - 5s) / (s + 1)$
Simplify Fraction: Simplify the fraction if possible. $\newline$ In this case, the numerator and the denominator have no common factors other than $1$ , so the fraction is already in its simplest form.

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