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Answer:
The operations follow the exact same rules, since rational expressions are fractions. You still need common denominators to add and subtract rational expressions just like you do for numerical fractions. You can multiply rational expressions by simply multiplying the numerators together and then multiplying the denominators together. You can divide rational expressions by multiplying the first one by the reciprocal of the second and then following the multiplication rules. You can even cancel common terms from the numerator and denominator like in numerical fractions. If you understand how to manipulate numerical fractions, then you can manipulate rational expressions because they follow the same rules. (Another name for a fraction is a rational number.) First of all, school is real life. You're there aren't you? You might use this skill in "real life" when setting up a proportion and there is an unknown value.
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How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions?
If you know how to do arithmetic with rational numbers you will understand the arithmetic with rational functions! Doing operations (adding, subtracting, multiplying, and dividing) is very similar. When you are
adding or subtracting they both require a common denominator. When multiplying or dividing it works the same for instance reducing by factoring.
Operations on rational expressions is similar to doing operations on fractions. You have to come up with a common denominator in order to add or subtract. To multiply the numerators and denominators separated. In division you flip the second fraction and multiply. The difference is that rational expressions can have variable letters and powers in them.
They're similar in that in doing addition and subtraction, you'll have to convert to common denominators. They're also similar in that you can't have a denominator of zero. They're different in that a rational expression is an algebraic expression of the form a/b, and a and b will be simpler expressions; for example a is 1 and b is x - 1 then the rational expression is 1/(x - 1). I think that understanding how to solve one type helps with skill in doing the other type. Fractions and rational expressions are used in buying and selling, measuring, designing, inventing, computer programming, accounting, and many other uses in real life.