Question

multiply. write your answer in simplest form. (\frac{x^2}{7} cdot \frac{7x - 28}{x^2})

Explanation:

Step1: Factor the numerator of the second fraction

First, we factor the numerator \(7x - 28\) of the second fraction. We can factor out a 7 from both terms: \(7x - 28 = 7(x - 4)\). So the expression becomes \(\frac{x^{2}}{7}\cdot\frac{7(x - 4)}{x^{2}}\).

Step2: Cancel out common factors

Now, we look for common factors in the numerators and denominators. The \(x^{2}\) in the numerator of the first fraction and the \(x^{2}\) in the denominator of the second fraction cancel out. Also, the 7 in the numerator of the second fraction and the 7 in the denominator of the first fraction cancel out. After canceling these common factors, we are left with \(x - 4\).

Answer:

\(x - 4\)