Question

1. \\(\frac{50x^3 - 70x^2}{70 - 50x} \cdot \frac{7x}{10x^2}\\)

Explanation:

Step1: Factor numerators and denominators

Factor \(50x^3 - 70x^2\) as \(10x^2(5x - 7)\), \(70 - 50x\) as \(-10(5x - 7)\), and keep the other fractions as is:
\(\frac{10x^2(5x - 7)}{-10(5x - 7)} \cdot \frac{7x}{10x^2}\)

Step2: Cancel common factors

Cancel \(10x^2\) from the first numerator and third denominator, and cancel \((5x - 7)\) from the first numerator and second denominator:
\(\frac{\cancel{10x^2}\cancel{(5x - 7)}}{-10\cancel{(5x - 7)}} \cdot \frac{7x}{\cancel{10x^2}}=\frac{7x}{-10}\)

Step3: Simplify the sign

Rewrite \(\frac{7x}{-10}\) as \(-\frac{7x}{10}\) (or \(\frac{-7x}{10}\))

Answer:

\(-\frac{7x}{10}\) (or \(\frac{-7x}{10}\))