Multiply. Write your answer in simplest form. s - 3/3s - 1 * 3s - 1/s^2 - 3s ______

Identify expressions to multiply: Identify the expressions to be multiplied. We have (s - 3)/(3s - 1) * (3s - 1)/(s^2 - 3s). We will multiply these two fractions.Multiply numerators and denominators: Multiply the numerators and the denominators. When multiplying fractions, we multiply the numerators together and the denominators together. (s - 3)/(3s - 1) * (3s - 1)/(s^2 - 3s) = ((s - 3) * (3s - 1)) / ((3s - 1) * (s^2 - 3s))Factor denominator of second fraction: Factor the denominator of the second fraction. The denominator s^2 - 3s can be factored by taking out the common factor s. s^2 - 3s = s(s - 3)Rewrite with factored denominator: Rewrite the expression with the factored denominator. (s - 3)/(3s - 1) * (3s - 1)/(s^2 - 3s) becomes (s - 3)/(3s - 1) * (3s - 1)/(s(s - 3))Cancel common factors: Cancel out common factors. We can cancel out (s - 3) and (3s - 1) from the numerator and denominator. (s - 3)/(3s - 1) * (3s - 1)/(s(s - 3)) = 1/s

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Math Problems

Algebra 2

Multiply and divide rational expressions

Full solution

Q. Multiply. Write your answer in simplest form.

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\frac{s - 3}{3s - 1} \times \frac{3s - 1}{s^2 - 3s}

Identify expressions to multiply: Identify the expressions to be multiplied. $\newline$ We have $(s - 3)/(3s - 1) \times (3s - 1)/(s^2 - 3s)$ . We will multiply these two fractions.
Multiply numerators and denominators: Multiply the numerators and the denominators. $\newline$ When multiplying fractions, we multiply the numerators together and the denominators together. $\newline$ $(s - 3)/(3s - 1) \times (3s - 1)/(s^2 - 3s) = ((s - 3) \times (3s - 1)) / ((3s - 1) \times (s^2 - 3s))$
Factor denominator of second fraction: Factor the denominator of the second fraction. $\newline$ The denominator $s^2 - 3s$ can be factored by taking out the common factor $s$ . $\newline$ $s^2 - 3s = s(s - 3)$
Rewrite with factored denominator: Rewrite the expression with the factored denominator. $(s - 3)/(3s - 1) \times (3s - 1)/(s^2 - 3s)$ becomes $(s - 3)/(3s - 1) \times (3s - 1)/(s(s - 3))$
Cancel common factors: Cancel out common factors. $\newline$ We can cancel out $(s - 3)$ and $(3s - 1)$ from the numerator and denominator. $\newline$ $\frac{s - 3}{3s - 1} \times \frac{3s - 1}{s(s - 3)} = \frac{1}{s}$