Question

1. \\(\frac{2m^2}{2m^3 - 14m^2} \cdot \frac{5m}{7m}\\)

Explanation:

Step1: Factor the denominator

Factor \(2m^3 - 14m^2\) as \(2m^2(m - 7)\). So the expression becomes \(\frac{2m^2}{2m^2(m - 7)} \cdot \frac{5m}{7m}\).

Step2: Simplify fractions

Cancel common factors: \(2m^2\) in numerator and denominator cancels, \(m\) in numerator and denominator of the second fraction cancels. We get \(\frac{1}{m - 7} \cdot \frac{5}{7}\).

Step3: Multiply fractions

Multiply the numerators and denominators: \(\frac{1\times5}{(m - 7)\times7}=\frac{5}{7(m - 7)}\) (or \(\frac{5}{7m - 49}\) after distributing the 7).

Answer:

\(\frac{5}{7(m - 7)}\) (or \(\frac{5}{7m - 49}\))