Final answer:
To distribute both fractions, you multiply the numerators and denominators individually and simplify by canceling common factors. This is applied separately to (x/y)(x/y - r/x) and -(r/x)(x/y - r/x), resulting in two distributed expressions.
Step-by-step explanation:
The process of distributing fractions that involve variables is a fundamental arithmetic procedure in algebra. When you need to distribute fractions, just multiply the numerators together and multiply the denominators together, and then simplify the expression by canceling out any common factors. This is a simple way to handle operations with algebraic fractions.
For the given problems, we have two separate distributions:
1) (x/y) multiplied by ((x/y) - (r/x))
2) -(r/x) multiplied by ((x/y) - (r/x)).
To perform the distribution, in the first case, you would multiply (x/y) by (x/y) and also (x/y) by -(r/x). Then, in the second case, multiply -(r/x) by (x/y) and -(r/x) by -(r/x). Remember that the units of the numerator in one fraction will be canceled by the units of the denominator of the following fraction, leaving only the desired unit for the result.
By following these steps and simplifying, you arrive at the distributed form for both expressions. Remember to always perform the arithmetic operations carefully, ensuring that you are consistent with signs and units throughout the calculation.