Question

divide and simplify.\\(\frac{m^{2}-p^{2}}{z - y}div\frac{m - p}{z - y}\\)\\(\frac{m^{2}-p^{2}}{z - y}div\frac{m - p}{z - y}=square\\)

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{m^2 - p^2}{z - y} \div \frac{m - p}{z - y}=\frac{m^2 - p^2}{z - y}\times\frac{z - y}{m - p}\)

Step2: Factor the difference of squares

We know that \(m^2 - p^2=(m + p)(m - p)\) (by the formula \(a^2 - b^2=(a + b)(a - b)\) where \(a = m\) and \(b = p\)). Substituting this into the expression, we get \(\frac{(m + p)(m - p)}{z - y}\times\frac{z - y}{m - p}\)

Step3: Cancel out common factors

The \((z - y)\) terms in the numerator and denominator cancel out, and the \((m - p)\) terms also cancel out. So we are left with \(m + p\)

Answer:

\(m + p\)