Is there any difference between multiplying fractions and multiplying rational functions? What is it?
Yes, there is a difference between multiplying fractions and multiplying rational functions.
When multiplying fractions, you simply multiply the numerators together and the denominators together. For example, if you have the fraction 3/4 and you multiply it by the fraction 2/5, you would multiply 3 * 2 to get the numerator, and 4 * 5 to get the denominator. The result would be 6/20, which can be simplified to 3/10.
On the other hand, when multiplying rational functions, you need to follow a different process. A rational function is a ratio of two polynomials. To multiply two rational functions, you multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. However, the process doesn't end there. After multiplying, you have to simplify the resulting fraction by factoring both the numerator and denominator, then canceling out any common factors. This step is important to ensure that the rational function is in its simplest form.
So, while the basic concept of multiplying fractions and multiplying rational functions involves multiplying the numerators and denominators, the difference lies in the additional steps required to simplify the resulting fraction when dealing with rational functions.