Algebraic simplification involves rewriting expressions to make them easier to work with or understand. The key is to maintain the equality of the expression while making it more straightforward. This is often done by distributing, combining like terms, or canceling common factors.
In this exercise, we simplified the expression \(\frac{1-x}{xy}\). The primary steps involved:
- Identifying the numerator and denominator correctly.
- Distributing the denominator over the numerator.
- Simplifying each term individually.
Starting with \(\frac{1-x}{xy}\), this can be split into \(\frac{1}{xy} - \frac{x}{xy}\). Rewriting it this way helps to see that further simplification leads to \(\frac{1}{xy} - \frac{1}{y}\), which is option a. Effectively breaking down expressions is a powerful algebraic skill.
Remember, careful distribution and term-by-term simplification can reveal the cleanest form of an algebraic expression.