91Ó°ÊÓ

Fractions are a way to represent parts of a whole. They consist of a numerator and a denominator. The numerator is the top part that indicates how many parts we have, whereas the denominator is the bottom part that tells us into how many equal parts the whole is divided.
In mathematics, fractions are extremely useful for representing values between integers.
For example, in the expression \(\frac{y+2}{y-2} \), "\(y+2\)" is the numerator and "\(y-2\)" is the denominator. Fractions can also be multiplied, divided, added, or subtracted. When multiplying fractions, as in our case, you simply multiply the numerators together and the denominators together, which can often lead to an opportunity for simplification.

The commutative property states that changing the order of numbers in an operation does not affect the result. This is true for addition and multiplication.
For example, in our expression, we observe \(\frac{y+2}{y-2} \cdot \frac{(y-2)^{2}}{y+2} \) can be rearranged as \(\frac{(y-2)^{2}}{y+2} \cdot \frac{y+2}{y-2} \) without changing the outcome. This property allows for flexibility when solving mathematical problems.
It's beneficial when simplifying expressions, as it lets us strategically cancel out terms.

The simplification rule is crucial for making expressions less complex and easier to work with. In mathematics, simplification involves reducing expressions to their simplest form.
In our example, simplifying \(\frac{y+2}{y-2} \cdot \frac{(y-2)^{2}}{y+2} \) means canceling out shared factors in the numerator and denominator.
Here, the terms \((y+2)\) and \((y-2)\) appear in both sides of the fraction and thus can be canceled out.
This leaves us with just \((y-2)\), provided we adhere to the condition that allows this operation, namely that \(y\) doesn't equal 2 or -2, preventing undefined operations.

Division by zero is an operation that is undefined in mathematics. It occurs when the divisor (denominator) is zero, which means you are trying to divide something into zero parts.
In the context of simplifying expressions like \(\frac{y+2}{y-2} \cdot \frac{(y-2)^{2}}{y+2} \), we must ensure the denominators are not zero to avoid undefined results.
This means setting restrictions on \(y\), such as \(y eq 2\) and \(y eq -2\), to keep the expression valid. When preparing to simplify, always identify restrictions linked to division by zero to maintain the integrity and validity of your solution.