(5(m-3n))/(m-n)×(2(m-n))/(m-2n)

Write Given Expression: Write down the given expression. We are given the expression (5(m-3n))/(m-n) × (2(m-n))/(m-2n).Factor Out Common Terms: Factor out common terms if possible. In this case, we notice that (m-n) is a common term in both the numerator and the denominator. We can simplify the expression by canceling out the (m-n) terms. (5(m-3n))/(m-n) × (2(m-n))/(m-2n) = 5(m-3n) × 2/(m-2n)Multiply Numerators and Denominators: Multiply the numerators and denominators. Now we multiply the numerators together and the denominators together. 5(m-3n) × 2 = 10(m-3n) The denominator remains (m-2n).Simplify Expression: Simplify the expression. We now have 10(m-3n)/(m-2n). This is the simplified form of the expression, as there are no common factors that can be canceled out further.

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Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

\frac{5(m-3 n)}{m-n} \times \frac{2(m-n)}{m-2 n}

Write Given Expression: Write down the given expression. $\newline$ We are given the expression $\frac{5(m-3n)}{m-n} \times \frac{2(m-n)}{m-2n}$ .
Factor Out Common Terms: Factor out common terms if possible. $\newline$ In this case, we notice that $(m-n)$ is a common term in both the numerator and the denominator. We can simplify the expression by canceling out the $(m-n)$ terms. $\newline$ $\frac{5(m-3n)}{m-n} \times \frac{2(m-n)}{m-2n} = 5(m-3n) \times \frac{2}{m-2n}$
Multiply Numerators and Denominators: Multiply the numerators and denominators. $\newline$ Now we multiply the numerators together and the denominators together. $\newline$ $5(m-3n) \times 2 = 10(m-3n)$ $\newline$ The denominator remains $(m-2n)$ .
Simplify Expression: Simplify the expression. $\newline$ We now have $\frac{10(m-3n)}{(m-2n)}$ . This is the simplified form of the expression, as there are no common factors that can be canceled out further.